Dirichlet L-function

(ML 7.7.A1) Dirichlet distribution

Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.

From playlist Machine Learning

Math 139 Fourier Analysis Lecture 35: Dirichlet's theorem pt. 2

Dirichlet's theorem: reduction of the problem. Dirichlet L-function. Product formula for L-functions. Extension of the logarithm to complex numbers. Convergence of infinite products.

From playlist Course 8: Fourier Analysis

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

Math 139 Fourier Analysis Lecture 37: Dirichlet's theorem pt.4

Defining the logarithm of an L-function. Second reduction of the problem: proving non-vanishing of the L-function. Case of complex Dirichlet characters.

From playlist Course 8: Fourier Analysis

Math 139 Fourier Analysis Lecture 38: Finishing proof of Dirichlet's theorem

Showing the non-vanishing of the L-function for real Dirichlet characters. Approximation of L(1,X) with hyperbolic sums to finish the theorem.

From playlist Course 8: Fourier Analysis

Math 139 Fourier Analysis Lecture 36: Dirichlet's theorem pt. 3

Proof of the product formula for Dirichlet L-functions. Defining the logarithm of an L-function: technical proposition. Key lemma.

From playlist Course 8: Fourier Analysis

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

(ML 7.7) Dirichlet-Categorical model (part 1)

The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.

From playlist Machine Learning

(ML 7.8) Dirichlet-Categorical model (part 2)

The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.

From playlist Machine Learning

Representation theory: Dirichlet's theorem

In this talk we see how to use characters of finite abelian groups to prove Dirichlet's theorem that there are infinitely many primes in certain arithmetic progressions. We first recall Euler's proof that there are infinitely many primes, which is the simplest case of Dirichlet's proof. T

From playlist Representation theory

Introduction to number theory lecture 49. Dirichlet's theorem

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We give an overview of the proof of Dirichlet's theorem, and give some examples of Dirichle

From playlist Introduction to number theory (Berkeley Math 115)

Introduction to number theory lecture 52. Nonvanishing of L series at s=1.

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We sketch how to show that Dirichlet L functions do not vanish at s=1, completing the proo

From playlist Introduction to number theory (Berkeley Math 115)

(ML 8.5) Bayesian Naive Bayes (part 3)

When all the features are categorical, a naïve Bayes classifier can be made fully Bayesian by putting Dirichlet priors on the parameters and (exactly) integrating them out.

From playlist Machine Learning

Low moments of character sums - Adam Harper

Joint IAS/Princeton University Number Theory Seminar Topic: Low moments of character sums Speaker: Adam Harper Affiliation: University of Warwick Date: April 08, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

The Heat Equation: Lecture 4 - Oxford Mathematics 1st Year Student Lecture

The heat equation, also known as the diffusion equation, is central to many areas in applied mathematics. In this series of four lectures - this is the fourth - forming part of the first year undergraduate mathematics course, 'Fourier Series and PDEs', the heat equation is derived and the

From playlist Oxford Mathematics 1st Year Student Lectures: The Heat Equation

Alexandra Florea: The Ratios Conjecture over function fields

I will talk about some recent joint work with H. Bui and J. Keating where we study the Ratios Conjecture for the family of quadratic L-functions over function fields. I will also discuss the closely related problem of obtaining upper bounds for negative moments of L-functions, which allows

From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"

Calderon problem (Lecture 1) by Venkateswaran P Krishnan

DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by

From playlist Workshop on Inverse Problems and Related Topics (Online)

Lecture 16: Fejer’s Theorem and Convergence of Fourier Series

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=8IxHMVf3jcA&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

Anton Thalmaier: The geometry of subelliptic diffusions

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 Probability and Statistics

(ML 7.7.A2) Expectation of a Dirichlet random variable

How to compute the expected value of a Dirichlet distributed random variable.

From playlist Machine Learning