Ramanujan tau function

Ramanujan tau function and the Sato--Tate conjecture

From playlist Number Theory

Bertrand Eynard: Integrable systems and spectral curves

Usually one defines a Tau function Tau(t_1,t_2,...) as a function of a family of times having to obey some equations, like Miwa-Jimbo equations, or Hirota equations. Here we shall view times as local coordinates in the moduli-space of spectral curves, and define the Tau-function of a spect

From playlist Analysis and its Applications

Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 1.mov

Example problems involving the integral of u to the power negative 1 du.

From playlist Transcendental Functions

Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 2.mov

More example problems involving the integral of 1 over u, du.

From playlist Transcendental Functions

Transcendental Functions 19 The Function a to the power x.mp4

The function a to the power x.

From playlist Transcendental Functions

Chandrashekhar Khare, Serre's conjecture and computational aspects of the Langlands program

VaNTAGe Seminar, April 5, 2022 License: CC-BY-NC-SA Some relevant links: Edixhoven-Couveignes-de Jong-Merkl-Bosman: https://arxiv.org/abs/math/0605244 Ramanujan's 1916 paper: http://ramanujan.sirinudi.org/Volumes/published/ram18.pdf Delta's home page in the LMFDB: https://www.lmfdb.org/

From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)

Differential Equations | The Unit Step Function

We define the unit step function, find its Laplace transform, and give an example. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Laplace Transform

The Ramanujan Conjecture and some diophantine equations - Peter Sarnak

Speaker : Peter Sarnak Date and Time : Faculty Hall, IISc, Bangalore Venue : 25 May 12, 16:00 One of Ramanujan's most influential conjectures concerns the magnitude of the Fourier Coefficients of a modular form. These were made on the basis of his calculations as well as a far-reaching in

From playlist Public Lectures

Modular forms: Hecke operators for forms

This lecture is part of an online graduate course on modular forms. We extend Hecke operators from modular functions to modular forms. As an application we prove some of Ramanujan's conjectures for the Ramanujan tau function. For the other lectures in the course see https://www.youtube.c

From playlist Modular forms

Niebur Integrals and Mock Automorphic Forms - Wladimir de Azevedo Pribitkin

Wladimir de Azevedo Pribitkin College of Staten Island, CUNY March 17, 2011 Among the bounty of brilliancies bequeathed to humanity by Srinivasa Ramanujan, the circle method and the notion of mock theta functions strike wonder and spark intrigue in number theorists fresh and seasoned alike

From playlist Mathematics

Differential Equations | Convolution: Definition and Examples

We give a definition as well as a few examples of the convolution of two functions. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Differential Equations

The standard L-function of Siegel modular forms and applications (Lecture 2) by Ameya Pitale

PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga

From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019

MegaFavNumbers 262537412680768000

This video is a contribution to the #MegaFavNumbers project, which seems to have overlooked the number 262537412680768000 This number turns up because e to the power of pi times the square root of 163 is about 262537412680768743.99999999999925... with a spectacular sequence of 9s after t

From playlist Math talks

What are the Inverse Trigonometric functions and what do they mean?

👉 Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-

From playlist Evaluate Inverse Trigonometric Functions

Laurent Massoulié : Non-backtracking spectrum of random graphs: community detection and ...

Abstract: A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The non-backtracking matrix of a graph is indexed by its directed edges and can be used to count non-backtracking walks of a given length. It has been used recently in th

From playlist Combinatorics

Introduction to the Dirac Delta Function

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to the Dirac Delta Function

From playlist Differential Equations

The Tau of Ramanujan by Eknath Ghate

KAAPI WITH KURIOSITY THE TAU OF RAMANUJAN SPEAKER: Eknath Ghate (TIFR, Mumbai) WHEN: 4pm to 6pm Sunday, 10 February 2019 WHERE: J. N. Planetarium, Sri T. Chowdaiah Road, High Grounds, Bangalore The sequence of numbers 1, -24, 252, -1472, 4830, ... was extensively studied by the great

From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)

Rogers-Ramanujan Identities | Part 3: More on partition generating functions.

We look more at partition generating functions, focusing on what each part of the generating function means in terms of the allowed partitions given some restriction. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Rogers-Ramanujan Identities

Scott Ahlgren: Algebraic and transcendental formulas for the smallest parts function

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