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#L-functions

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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
Institute for Advanced Study

On the Kudla-Rapoport Conjecture - Chao Li

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Explore the Kudla-Rapoport conjecture, Hurwitz class numbers, and their connections to Eisenstein series and L-functions in this advanced number theory seminar by Chao Li.
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16 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Hidden Symmetries of the Work of Jan Nekovář

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Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Galois Representations and Statistics - Lecture 1

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Explore Galois representations and statistics in arithmetic through an advanced mathematical lecture by René Schoof.
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1 Lesons
1 hour
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
ICTP Mathematics

Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art

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Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.
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10 Lesons
55 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Valentin Blomer - The Polynomial Method for Point Counting and Exponential Sums, Lecture III

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Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.
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10 Lesons
45 minutes
On-Demand
Free-Video
Fields Institute

Eisenstein Cocycles and Values of L-Functions

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Explore Eisenstein cocycles, equivariant cohomology, and their applications to L-functions. Gain insights into recent constructions and their connections to theta kernels and arithmetic groups.
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16 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Quantum Complexity and L-functions

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Explore quantum algorithms for L-functions and zeta functions, examining complexity results, cohomology's role, and applications to modular forms and Mordell-Weil theorem.
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18 Lesons
55 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Siegel Modular Forms - Classical and Adelic Aspects by Ameya Pitale

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Explore Siegel modular forms from classical and modern perspectives, including functions on Siegel upper half spaces and automorphic representations of the symplectic group.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
IMSA

Extensions of Hodge Structure and Completions of Fundamental Groups

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Explore extensions of mixed Hodge structures, unipotent and relative completions of fundamental groups, and their geometric interpretations in L-functions and motives theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Mathematical Union

The Distribution of Values of Zeta and L-Functions

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Explore the intricate world of zeta and L-functions, delving into their value distribution patterns and mathematical implications with renowned number theorist Kannan Soundararajan.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Orbit Method, Microlocal Analysis and Applications to L-Functions

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Explore quantitative orbit method in microlocal analysis, its applications to representation theory, and implications for L-functions, including moment estimates and subconvex bounds.
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1 Lesons
57 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Ratios Conjecture Over Function Fields

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Explore the Ratios Conjecture for quadratic L-functions over function fields, including upper bounds for negative moments and partial results for various L-function ratios.
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1 Lesons
59 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 18

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Explore the Langlands Program through automorphic forms and representation theory, delving into advanced mathematical concepts and their interconnections.
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1 Lesons
1 hour 3 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
IMSA

Eigenvarieties and Arithmetic - Connection to L-Functions

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Explore eigenvarieties, p-adic automorphic forms, and their connection to L-functions. Discover the local geometry of eigenvarieties and its significance in arithmetic.
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1 Lesons
57 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

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
Hausdorff Center for Mathematics

Beilinson's Conjecture for the Dwork Family

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Explores Beilinson's conjecture for the Dwork family, focusing on constructing classes in higher Chow groups and computing their regulators in relation to motivic L-functions and automorphic forms.
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1 Lesons
54 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Motivic Galois Theory of Algebraic Mellin Transforms

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Explore the intricate connections between algebraic geometry and number theory through the lens of motivic Galois theory and Mellin transforms.
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1 Lesons
41 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modularity and Monodromy

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Explore the intricate relationship between modularity and monodromy in mathematics, delving into advanced concepts and their applications in number theory and algebraic geometry.
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1 Lesons
1 hour 16 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
Centre International de Rencontres Mathématiques

Motives and Automorphic Representations

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Explore motives and automorphic representations in advanced mathematics with James Arthur's insightful conference talk at CIRM.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Zeta Functions of Shimura Varieties: Past, Present, and the Near Future

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Explore Zeta functions of Shimura varieties, covering historical developments, current research, and future directions in this advanced mathematical topic.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Computing Euler Factors of Curves

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Explore computational methods for determining Euler factors of curves in arithmetic geometry, focusing on advanced mathematical techniques and applications.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Frobenius Distributions - Lecture 1

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Explore Frobenius distributions in arithmetic statistics through an advanced mathematical lecture by Kiran Kedlaya at CIRM's Spring School.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Period Relations for Arithmetic Automorphic Periods on Unitary Groups

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Explore period relations for arithmetic automorphic periods on unitary groups, focusing on Petersson inner products and connections to L-function special values.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Conjectures on L-functions for Varieties over Function Fields and Their Relations

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Explore conjectures on L-functions for varieties over function fields, focusing on abelian varieties and the BSD-rank conjecture. Examine relationships using rigid cohomology.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Banach Center

Mathematical Grand Unification

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Explore the concept of mathematical grand unification through a thought-provoking lecture by Bartosz Naskręcki, delving into conjectures and potential connections across mathematical fields.
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1 Lesons
1 hour 10 minutes
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
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

Average Heights of Abelian Varieties with Complex Multiplication

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Explore the arithmetic properties of abelian varieties with complex multiplication, focusing on Colmez's conjecture and its implications for periods and L-functions.
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1 Lesons
50 minutes
On-Demand
Free-Video
BIMSA

Heights of Algebraic Cycles and Special Values of L-Series - ICBS 2024

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Explore heights of algebraic cycles and their connections to L-series special values, focusing on CM points and Gross-Schoen cycles on elliptic curves.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
BIMSA

Riemann Hypothesis for Plane Curve Singularities

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Explore the Riemann Hypothesis for plane curve singularities through motivic superpolynomials. Delve into L-functions, DAHA-superpolynomials, and their applications in number theory and geometry.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

A Statistical Physics Approach to the Sine Beta Process and Other Random Point Processes

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Explore statistical physics approaches to Sine Beta processes and random point systems, focusing on universality properties and applications of DLR tools.
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1 Lesons
54 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

Towards a Formulation of the Birch and Swinnerton-Dyer Conjecture for Abelian Schemes Over Varieties Over Finite Fields

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Delve into advanced number theory concepts exploring the Birch and Swinnerton-Dyer conjecture's formulation for abelian schemes over finite field varieties, presented by mathematician Amilcar Pacheco.
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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
Centre International de Rencontres Mathématiques

Vanishing of Twisted L-Functions of Elliptic Curves Over Function Fields

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Explore vanishing of twisted L-functions for elliptic curves over function fields, focusing on rich characters, Honda Theory, and Legendre Theory in this advanced mathematical discussion.
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12 Lesons
46 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
Instituto de Matemática Pura e Aplicada

L-functions of Elliptic Curves Over Real Quadratic Fields as Special Values of Automorphic Green's Functions

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Delve into advanced number theory concepts exploring L-functions of elliptic curves over real quadratic fields and their relationship to automorphic Green's functions through expert mathematical analysis.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
BunG Seminar

Introduction to the Tamagawa Number Theorem for Function Fields

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Delve into advanced number theory concepts through an exploration of Tamagawa numbers, their role in lattice enumeration, L-functions, and geometric interpretations in function fields.
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1 Lesons
1 hour 51 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

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

Level Aspect Subconvexity for GL2×GL2 L-functions

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Delve into advanced number theory concepts focusing on level aspect subconvexity for GL2xGL2 L-functions, exploring circle method applications and analytic theory developments.
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1 Lesons
49 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

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