Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
A. von Pippich - An analytic class number type formula for PSL2(Z)
For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H instead of prime numbers. In this talk, we report on a formula that determines the special value a
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Some identities involving the Riemann-Zeta function.
After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Number Theory 1.1 : Product Formula for the Zeta Function
In this video, I prove Euler's product formula for the Riemann Zeta function. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
Monotonicity of the Riemann zeta function and related functions - P Zvengrowski [2012]
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences May 17, 2012 14:00, St. Petersburg, POMI, room 311 (27 Fontanka) Monotonicity of the Riemann zeta function and related functions P. Zvengrowski University o
From playlist Number Theory
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming
Peter Sarnak - The Selberg Integral, Rankin Selberg Method, Arithmeticity [2008]
http://www.ams.org/notices/200906/rtx090600692p-corrected.pdf Saturday, January 12 12:00 PM Peter Sarnak The Selberg Integral, Rankin Selberg Method, Arithmeticity Atle Selberg Memorial Memorial Program in Honor of His Life & Work January 11-12, 2008 Renowned Norwegian mathematician A
From playlist Number Theory
Kannan Soundararajan - Selberg's Contributions to the Theory of Riemann Zeta Function [2008]
http://www.ams.org/notices/200906/rtx090600692p-corrected.pdf January 11, 2008 3:00 PM Peter Goddard, Director Welcome Kannan Soundararajan Selberg's Contributions to the Theory of Riemann Zeta Function and Dirichlet L-Functions Atle Selberg Memorial Memorial Program in Honor of His
From playlist Number Theory
Jon Keating: Random matrices, integrability, and number theory - Lecture 3
Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp
From playlist Analysis and its Applications
Wim Veys : Zeta functions and monodromy
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
The Generalized Ramanujan Conjectures and Applications - Lecture 1 by Peter Sarnak
Lecture 1: The Generalized Ramanujan Conjectures Abstract: One of the central problems in the modern theory of automorphic forms is the Generalized Ramanujan Conjecture.We review the development and formulation of these conjectures as well as recent progress. While the general Conjecture
From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
The distribution of values of zeta and L-functions
50 Years of Number Theory and Random Matrix Theory Conference Topic: The distribution of values of zeta and L-functions Speaker: Kannan Soundararajan Affiliation: Stanford University Date: June 21, 2022 I will survey recent progress on understanding the value distribution of zeta and L-f
From playlist Mathematics
Peter Sarnak, Summation formulae in spectral theory and number theory [2021]
A talk in honor of Zeev Rudnick's 60th birthday Peter Sarnak, Summation formulae in spectral theory and number theory (Institute for Advanced Study and Princeton University) Abstract: The Poisson Summation formula, Riemann-Guinand-Weil explicit formula, Selberg Trace Formula and Lefsche
From playlist Number Theory
Opening Remarks and History of the math talks - Peter Sarnak, Hugh Montgomery and Jon Keating
50 Years of Number Theory and Random Matrix Theory Conference Topic: Opening Remarks and History of the math talks Speakers: Peter Sarnak, Hugh Montgomery and Jon Keating Date: June 21 2022
From playlist Mathematics
Valentin Blomer - 4/4 Automorphic forms in higher rank
Valentin Blomer - Automorphic forms in higher rank
From playlist École d'été 2014 - Théorie analytique des nombres
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
Large deviation estimates for Selberg’s central limit theorem, applications, and..... - Emma Bailey
50 Years of Number Theory and Random Matrix Theory Conference Large deviation estimates for Selberg’s central limit theorem, applications, and numerics Speaker: Emma Bailey Affiliation: City University of New York June 22, 2022 Selberg’s celebrated central limit theorem shows that the lo
From playlist Mathematics