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#Riemann Zeta Function

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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
3Blue1Brown

Visualizing the Riemann Zeta Function and Analytic Continuation

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Explore the Riemann zeta function's visualization, analytic continuation, and its connection to the famous Riemann hypothesis through engaging animations and clear explanations.
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10 Lesons
22 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Time and Band Limiting for Exceptional Orthogonal Polynomials

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Explore time-and-band limiting in exceptional orthogonal polynomials, connecting integral operators, differential equations, and bispectral problems. Uncover links to KdV equations and random matrix theory.
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1 Lesons
57 minutes
On-Demand
Free-Video
Physics Explained

What Is the Riemann Hypothesis?

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Explore the Riemann Hypothesis, convergent series, and Euler's solutions in this engaging introduction to complex mathematical concepts and their implications.
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15 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

The Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths

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Explores the divide between exact and approximate theories in pure mathematics, challenging conventional views on arithmetic, algebra, topology, and number theory, including the Riemann Hypothesis.
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7 Lesons
41 minutes
On-Demand
Free-Video
Michael Penn

More Identities Involving the Riemann-Zeta Function

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Explore combinatorial techniques to derive new identities for the Riemann-Zeta function, building on previous mathematical concepts and expanding analytical understanding.
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1 Lesons
23 minutes
On-Demand
Free-Video
Michael Penn

Some Identities Involving the Riemann-Zeta Function

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Explore the Riemann-Zeta function, its generating function for positive even integers, and derive sum identities in this mathematical deep dive.
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1 Lesons
26 minutes
On-Demand
Free-Video
Michael Penn

Another Riemann-Zeta Function Identity

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Explore an intriguing identity involving even values of the Riemann-Zeta function, delving into limits, sums, and transformations to uncover mathematical insights.
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7 Lesons
29 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Finite Part of Infinity by Joseph Samuel

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Explore the paradoxical equation 1+2+3...=-1/12, its mathematical interpretation, and its impact on physics, including the Casimir effect, with insights from differential geometry and topology.
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19 Lesons
1 hour 35 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
IMSA

A Construction of Apéry Constants from Landau Ginzberg Models

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Explores construction of Apéry constants from Landau-Ginzberg models, linking quantum differential equations of Fano threefolds to mirror symmetry and geometric higher normal functions.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Mathologer

Ramanujan - Making Sense of 1+2+3+... = -1/12 and Co.

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Explore the mathematical paradox of infinite sums equaling unexpected values, delving into Ramanujan's work, summation rules, and connections to the Riemann Zeta function.
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1 Lesons
35 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

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
Insights into Mathematics

Euler's Product for the Zeta Function via Box Arithmetic - Part 1

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Explore box arithmetic's application to number theory, focusing on the Euler product for the Riemann zeta function and the Fundamental Identity of Arithmetic in a combinatorial framework.
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1 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Multiplicative Functions and Dirichlet Series via Boxes - Part 2

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Explores Dirichlet series and box arithmetic, offering a novel approach to number theory concepts without relying on infinity. Introduces caretation and algebraic structures for encoding Dirichlet series.
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1 Lesons
37 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
Institut Henri Poincaré

Crystalline Measures and Zeta Functions

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Explorez les liens entre mesures cristallines et fonctions zêta, en examinant leurs propriétés et relations avec la fonction zêta de Riemann.
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1 Lesons
37 minutes
On-Demand
Free-Video
Schmid College, Chapman University

On a Function of G.H. Hardy and J.E. Littlewood

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Explore Hardy and Littlewood's series expansion, its broader context, and connections to Beurling's theorem and ternary quadratic forms' zeta functions.
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1 Lesons
43 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

A Journey from Statistical Mechanics to Number Theory

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Explore connections between statistical mechanics and number theory, focusing on the Riemann zeta function and its relation to phase transitions in disordered systems.
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1 Lesons
39 minutes
On-Demand
Free-Video
BIMSA

Euler's Constant and Exponential Motives

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Explore Euler's constant in exponential motives, examining its role in Q(-1) extensions and E-function differential equations.
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1 Lesons
1 hour 2 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
Wrath of Math

The Probability of Relatively Prime Numbers - A Mathematical Analysis

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Explore the fascinating probability of coprime numbers through infinite series, the Basel problem, and fundamental probability laws - all explained with clear mathematical reasoning.
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7 Lesons
19 minutes
On-Demand
Free-Video
Institute for Advanced Study

Duality of Fluid Mechanics and Solution of Decaying Turbulence

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Delve into advanced fluid dynamics theory, exploring momentum loop equations, string theory applications, and analytical solutions for decaying turbulence spectrum through mathematical physics principles.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video