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#Analytic Number Theory

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Institute for Advanced Study

Second Moment of the GL_3 Standard L-function on the Critical Line

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Explore advanced number theory concepts, focusing on GL_3 L-functions, moments of the Riemann zeta function, and applications to the Rankin-Selberg problem.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 2

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Explore advanced concepts in subconvexity of L-functions through an in-depth mathematical lecture by Philippe Michel, expanding on previous discussions.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Spectra of Some Arithmetical Matrices

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Explore the spectral analysis of GCD matrices and their connection to analytic number theory, focusing on recent developments in this classical field.
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1 Lesons
53 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Riemann Hypothesis and the DeBruijn-Newman Constant

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Delve into advanced mathematical concepts exploring the Riemann Hypothesis and DeBruijn-Newman constant through expert analysis of their properties, relationships, and significance in number theory.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
ICTP Mathematics

On the Riemann Zeta-Function, Fourier Optimization and Quadratic Forms

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Explore the Riemann zeta-function, Fourier analysis, and quadratic forms in number theory. Delve into Selberg's theorem, Berry's conjecture, and representation of integers by quadratic forms.
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9 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Jonathan Hickman- On Littlewood-Paley Theory for Space Curves

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Explore Littlewood-Paley inequalities for functions with Fourier transforms near submanifolds, focusing on space curves and applications in harmonic analysis, PDE, and number theory.
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1 Lesons
45 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

New Avenues for the Circle Method - Lecture I

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Explore adelic delta-method and nonabelian analogues in analytic number theory. Discover Poisson summation formulae for special varieties to generalize Fourier theory techniques.
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1 Lesons
59 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Terence Tao - Pseudorandomness of the Liouville Function

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Explore the Liouville pseudorandomness principle and its related conjectures, examining recent progress in understanding the statistical behavior of the Liouville function in number theory.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Relative Trace Formulas for GL - 2 - and Analytic Number Theory

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Explore relative trace formulas for GL(2) and their applications in analytic number theory, delving into advanced mathematical concepts and techniques.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
ICTP Mathematics

Basic Notions Seminar on Fourier Optimization and Number Theory

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Explore the intersection of harmonic analysis and analytic number theory, including problems related to the Riemann hypothesis, in this advanced mathematics seminar.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Fields Institute

Primes, Postdocs and Pretentiousness - 2021 CRM-Fields-PIMS Prize Lecture

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Explore prime numbers, academic careers, and mathematical concepts in this engaging lecture by renowned mathematician Andrew Granville, offering insights into number theory and research.
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1 Lesons
59 minutes
On-Demand
Free-Video
Fields Institute

Akshay Venkatesh: The Great Connector - Fields Medal Symposium 2022

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Explore Akshay Venkatesh's groundbreaking work connecting diverse mathematical fields and his insights on the evolving nature of mathematical research in the digital age.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 2

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Explore advanced topics in linear groups and Diophantine approximation, focusing on bounded generation and its applications in number theory and geometric analysis.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 3

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Explore advanced concepts in linear groups and Diophantine approximation, focusing on bounded generation techniques and their applications in number theory and geometric analysis.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Central Extensions of Arithmetic Lattices by Matthew Stover

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Explore central extensions of arithmetic lattices, focusing on techniques from algebraic and analytic number theory. Gain insights into applications in geometry, topology, and mathematical physics.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Conjugacy Width in Higher Rank Arithmetic Groups of Orthogonal Type by Chen Meiri

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Explore conjugacy width in higher rank arithmetic groups of orthogonal type, examining its properties and implications for group theory and related mathematical fields.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Hasse Principle for Reductive Algebraic Groups Over Finitely Generated

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Explore the Hasse Principle for reductive algebraic groups over finitely generated fields, delving into advanced number theory and algebraic geometry concepts.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Fields Institute

Some Research Problems in Number Theory

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Explore intriguing research problems in number theory with Ram Murty, delving into advanced mathematical concepts and unsolved questions in this fascinating field.
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1 Lesons
43 minutes
On-Demand
Free-Video
Fields Institute

A Survey of Central Limit Theorems in Number Theory

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Explore key central limit theorems in number theory, examining their applications and implications for understanding mathematical distributions and patterns.
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1 Lesons
36 minutes
On-Demand
Free-Video
Fields Institute

A Simple Proof of the Wiener-Ikehara Tauberian Theorem

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Explore a concise demonstration of the Wiener-Ikehara Tauberian Theorem, a fundamental result in analytic number theory with wide-ranging applications.
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1 Lesons
40 minutes
On-Demand
Free-Video
Fields Institute

The Eighth and Shifted Moments of the Riemann Zeta Function

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Explore advanced mathematical concepts related to the Riemann zeta function, focusing on its eighth and shifted moments in this specialized lecture by Peng-Jie Wong.
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1 Lesons
34 minutes
On-Demand
Free-Video
Fields Institute

Quantum Unique Ergodicity for Powerful Level via Shifted Convolution Sum

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Explore advanced mathematical concepts in number theory, focusing on QUE for powerful levels using shifted convolution sum techniques.
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1 Lesons
33 minutes
On-Demand
Free-Video
Fields Institute

One-level Densities in Families of Grossencharakters Associated to CM Elliptic Curves

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Explore one-level densities in Grossencharakters families linked to CM elliptic curves, delving into advanced number theory concepts and their applications.
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1 Lesons
35 minutes
On-Demand
Free-Video
Fields Institute

Analytic Number Theory and Automorphic Forms

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Explore advanced concepts in analytic number theory and automorphic forms with insights from a renowned expert in the field.
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1 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

Multiplicative Functions and Dirichlet Series via Boxes - Math Foundations 242

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Explore multiplicative functions and Dirichlet series using the Fundamental Identity of Arithmetic. Discover interesting mathematical identities and their connections to analytic number theory.
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1 Lesons
26 minutes
On-Demand
Free-Video
Wolfram

Computational Number Theory in the Modern World

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Explore modern computational number theory, covering primes, factorization, divisibility, congruence, and advanced topics like analytic and additive number theory.
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17 Lesons
26 minutes
On-Demand
Free-Video
Dr Trefor Bazett

Euler Product Formula - A Beautiful Equation in Number Theory

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Discover the beauty of the Euler Product Formula, connecting sums over natural numbers to products over primes. Explore its proof, applications, and links to the Riemann Hypothesis.
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5 Lesons
17 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 3

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Explore advanced concepts in subconvexity of L-functions with mathematician Paul Nelson in this in-depth conference talk from the "Building bridges 6th EU/US" meeting.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 1

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Explore advanced concepts in analytic number theory, focusing on subconvexity bounds for L-functions and their applications in mathematics.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 4

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Explore advanced concepts in subconvexity of L-functions with mathematician Paul Nelson in this in-depth conference talk from the "Building bridges 6th EU/US" meeting.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
NCCR SwissMAP

Zeta Functions for Anosov Diffeomorphisms, Flows and Actions

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Explore analytic techniques in dynamics and geometry, focusing on zeta functions for Anosov diffeomorphisms, flows, and actions.
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1 Lesons
56 minutes
On-Demand
Free-Video
Banach Center

Analytic Methods in Arithmetic

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Explore advanced analytic techniques in arithmetic, focusing on their applications and theoretical foundations in number theory.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Sums of the Divisor Function and Random Matrix Distributions - Lecture

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Explore divisor function behavior, distribution strategies, and connections to Riemann zeta function and random matrix groups in number theory.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Magic of the Primes

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Explore the fascinating world of prime numbers, their importance in mathematics and real-world applications, and recent progress on ancient mathematical questions.
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1 Lesons
1 hour
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

What is an L-function? - An Introduction to Zeta and L-functions in Number Theory

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Explore the evolution of L-functions from Euler to Langlands, understanding their crucial role in prime number distribution and mathematical research.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

Eisenstein Series - An Overview

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Explore Eisenstein series in a concise, self-contained overview, gaining insights into this mathematical concept and its applications.
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1 Lesons
48 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Branching Processes in Random Matrix Theory and Analytic Number Theory

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Explore branching processes in random matrix theory and analytic number theory, focusing on limiting distributions, log-correlated phenomena, and recent conjectures about maxima of characteristic polynomials and L-functions.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
BIMSA

Weyl-Strength Subconvexity for Dirichlet L-Functions

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Explore Weyl-strength subconvexity for Dirichlet L-functions, examining the subconvexity problem and progress on obtaining the Weyl exponent via the method of moments.
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1 Lesons
51 minutes
On-Demand
Free-Video
BIMSA

Asymptotic Orthogonality Relation for GL(n,R) - ICBS 2024

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Explore generalized Dirichlet character orthogonality for GL(n,R), extending classical number theory to higher dimensions with applications.
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1 Lesons
55 minutes
On-Demand
Free-Video
BIMSA

Large Values of Zeta and Dirichlet L-Functions - ICBS 2024

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Explore large values of Riemann zeta and Dirichlet L-functions on the critical line, uncovering key insights in analytic number theory.
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1 Lesons
58 minutes
On-Demand
Free-Video
Banach Center

Diophantine Equations and Discrete Harmonic Analysis - Part 3

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Explore advanced concepts in Diophantine equations and discrete harmonic analysis, delving into complex mathematical theories and applications with expert Ákos Magyar.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Banach Center

Diophantine Equations and Discrete Harmonic Analysis - Part 4

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Explore advanced concepts in Diophantine equations and discrete harmonic analysis, delving into complex mathematical theories and applications with expert Ákos Magyar.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Banach Center

Diophantine Equations and Discrete Harmonic Analysis - Part 2

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Explore advanced concepts in Diophantine equations and discrete harmonic analysis, delving into complex mathematical theories and applications with expert Ákos Magyar.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Banach Center

Diophantine Equations and Discrete Harmonic Analysis - Part 1

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Explore Diophantine equations and discrete harmonic analysis with Ákos Magyar, delving into advanced mathematical concepts and their applications in number theory and analysis.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
TheIACR

Recovering Short Generators of Principal Ideals in Cyclotomic Rings

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Explore principal ideals in cyclotomic rings, focusing on short generator recovery techniques and their cryptographic implications. Gain insights from Oded Regev's expert analysis.
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13 Lesons
24 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Analytical Properties of Automorphic L-Series via its Integral Kernel

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Delve into advanced mathematical concepts exploring analytical properties of automorphic L-series through integral kernel analysis, presented by Fernando Andrés Herrera Contreras at IMPA's Number Theory Workshop.
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1 Lesons
27 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Modified Character Sums Over the k-Free Integers

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Delve into advanced number theory concepts with a focused exploration of modified character sums and their relationship to k-free integers in this mathematical research presentation.
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1 Lesons
14 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Remarks on a Formula of Ramanujan

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Delve into an advanced mathematical exploration of Ramanujan's formula through expert analysis and insights from Andrés Chirre of PUCP, examining its implications and applications in number theory.
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1 Lesons
34 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Kloosterman Sums Over Families of Lattices

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Delve into advanced mathematical concepts focusing on Kloosterman sums and their relationships with lattice families through expert analysis and theoretical exploration.
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1 Lesons
53 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Single-valued Integrals and Modular Forms

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Delve into advanced mathematical concepts exploring the relationship between single-valued integrals and modular forms, with applications in analytic number theory and complex analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Low Lying Zeros in Families Related to Complex Multiplication Elliptic Curves

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Delve into advanced number theory concepts focusing on low-lying zeros and their relationship to CM elliptic curves, exploring mathematical patterns and theoretical frameworks in this specialized mathematical domain.
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1 Lesons
51 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Arithmetical Exponential Sums - An Urchin Story

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Delve into advanced mathematical concepts of arithmetical exponential sums through an engaging exploration of their properties, patterns, and applications in number theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Reversible Primes

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Delve into the mathematical concept of reversible primes through an advanced number theory presentation exploring their properties, patterns, and significance in contemporary mathematical research.
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1 Lesons
50 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Moments of L-functions - Lecture 4

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Delve into advanced mathematical concepts of L-functions and their moments, exploring circle method applications in analytic number theory and related theoretical frameworks.
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1 Lesons
1 hour 47 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Applications of Delta Method in Number Theory - Lecture 2

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Delve into advanced number theory concepts through the Delta Method, exploring its applications in analytic theory and circle method techniques for solving complex mathematical problems.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Moments of L-functions - Lecture 3

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Delve into advanced analytic number theory with a focus on L-function moments, circle method applications, and their connections to rational points and prime number theory.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Classical Circle Method - Lecture 3

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Delve into advanced number theory concepts through the Classical Circle Method, exploring its applications in analytic theory and rational point counting on varieties.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Applications of Delta Method in Number Theory - Lecture 1

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Delve into advanced number theory concepts through the Delta Method, exploring its applications in analytic theory and circle method techniques for solving complex mathematical problems.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Exponential Sums - Lecture 2

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Delve into advanced number theory concepts through an exploration of exponential sums, circle method applications, and their role in analyzing rational points on varieties and prime number theory.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Sub-Weyl Bound for GL(2) L-functions

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Delve into advanced number theory concepts focusing on Sub-Weyl bounds for GL(2) L-functions, exploring circle method applications and their connections to analytic theory.
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1 Lesons
43 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Small Solutions of Generic Ternary Quadratic Congruences

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Delve into advanced number theory concepts focusing on small solutions of generic ternary quadratic congruences, exploring circle method applications and analytical approaches in modern mathematics.
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1 Lesons
50 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Subconvexity for L-functions of Hilbert Modular Forms via Delta Method

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Delve into advanced number theory concepts focusing on L-functions of Hilbert modular forms and their subconvexity bounds through the Delta Method approach in analytic number theory.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Relation Between Low-lying Zeros and Central Values

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Explore the intricate relationship between low-lying zeros and central values in number theory through advanced mathematical analysis and circle method applications.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Second Moment of the GL_3 Standard L-function on the Critical Line

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Delve into advanced number theory concepts focusing on GL_3 Standard L-function's second moment analysis on the critical line through rigorous mathematical exploration.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Subconvexity for Rankin-Selberg L-functions in Prime Power Level

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Delve into advanced number theory concepts focusing on Rankin-Selberg L-functions and their subconvexity bounds in prime power level, exploring circle method applications in analytic theory.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Systems of Many Forms with Differing Degrees

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Explore advanced circle method applications in number theory, focusing on rational point counting, prime numbers, and recent developments in L-functions and Langlands program theory.
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1 Lesons
56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Symptotics of the Second Moment of GL(3) Twisted L-functions

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Delve into advanced number theory concepts focusing on GL(3) twisted L-functions, their second moment asymptotics, and applications in the circle method within analytic number theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Biases Among Classes of Rank-crank Partitions Mod 11

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Delve into advanced number theory concepts focusing on rank-crank partition biases in modulo 11, exploring circle method applications and analytical approaches in partition theory.
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1 Lesons
32 minutes
On-Demand
Free-Video