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
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
Kenichi Bannai - Shintani generating class and the p-adic polylogarithm for totally real fields
The organizer is sorry for the technical problem that a part of the slides is hidden. In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke L-functions for totally real fields. In particular, we will construct
From playlist Conférences Paris Pékin Tokyo
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
Transcendental Functions 19 The Function a to the power x.mp4
The function a to the power x.
From playlist Transcendental Functions
on the Brumer-Stark Conjecture (Lecture 2) by Samit Dasgupta
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Mahesh Kakde: Brumer-Stark units and a conjecture of Gross
The existence of Brumer-Stark unit is guaranteed by the Brumer-Stark conjecture. A conjecture of Dasgupta gives an explicit p-adic analytic formula for these units. An approach to this explicit formula is given by the tower of fields conjecture of Gross. After recalling these conjecture an
From playlist Number Theory
Subconvexity of Shintani Zeta Functions - Eun Hye Lee
Joint Columbia-CUNY-NYU Number Theory Seminar Topic: Subconvexity of Shintani Zeta Functions Speaker: Eun Hye Lee Affiliation: Stony Brook University Date: October 7, 2021
From playlist Joint Columbia-CUNY-NYU Number Theory Seminar
On the Gross—Stark conjecture 1 by Mahesh Kakde
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
Claudia Alfes: Traces of CM values and geodesic cycle integrals of modular functions
In this talk we give an introduction to the study of generating series of the traces of CM values and geodesic cycle integrals of different modular functions. First we define modular forms and harmonic Maass forms. Then we briefly discuss the theory of theta lifts that gives a conceptual f
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
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
The average size of 3-torsion in class groups of 2-extensions - Robert Lemke Oliver
\Joint IAS/Princeton University Number Theory Seminar Topic: The average size of 3-torsion in class groups of 2-extensions Speaker: Robert Lemke Oliver Affiliation: Tufts University Date: April 07, 2022 We determine the average size of the 3-torsion in class groups of G-extensions of a n
From playlist Mathematics
Aurelien Sagnier: Towards arithmetic sites at some places
Talk by Aurelien Sagnier in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on July 08, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
On the Gross—Stark conjecture 2 by Mahesh Kakde
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
The Riemann Hypothesis - Picturing The Zeta Function
in this chapter i will show how to visualize the zeta and eta functions in the proper way meaning that everything on those two functions is made out of spirals all over the grid and the emphasis in this chapter will be on the center points of the spirals mainly the divergent spirals 0:00
From playlist Summer of Math Exposition Youtube Videos
Peter Sarnak - Zeta and L-functions [ICM 1998]
ICM Berlin Videos 27.08.1998 Zeta and L-functions Peter Sarnak Princeton University, USA: Number Theory Thu 27-Aug-98 · 11:45-12:45 h Abstract: The theory of zeta and L-functions is at the center of a number of recent developments in number theory. We will review some of these developm
From playlist Number Theory
Geometry-of-Numbers Techniques in Arithmetic Statistics (Lecture 3) by Arul Shankar
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
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