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 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 06: Convolutions and Approximations of the Identity, ct'd.
Convolutions and Good Kernels, continued. Interaction of convolution with Fourier transform (for integrable functions). Approximations of the Identity (family of good kernels). Recovery of the value of a function at a point of continuity using approximations of the identity. Uniform co
From playlist Course 8: Fourier Analysis
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
(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 05: Convolutions and Approximation of the Identity
Convolutions and Good Kernels. Definition of convolution. Convolution with the n-th Dirichlet kernel yields the n-th partial sum of the Fourier series. Basic properties of convolution; continuity of the convolution of integrable functions.
From playlist Course 8: Fourier Analysis
Polynomial approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Nikolay Moshchevitin: Diophantine exponents, best approximation and badly approximable numbers
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 23, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Why do prime numbers make these spirals? | Dirichlet’s theorem, pi approximations, and more
A curious pattern, approximations for pi, and prime distributions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/spiral-thanks Based on this Math
From playlist Neat proofs/perspectives
Approximating Irrational Numbers (Duffin-Schaeffer Conjecture) - Numberphile
James Maynard recently co-authored a proof of the Duffin-Schaeffer Conjecture. More links & stuff in full description below ↓↓↓ More James Maynard on Numberphile: http://bit.ly/JamesMaynard On the Duffin-Schaeffer conjecture - by Dimitris Koukoulopoulos and James Maynard - https://arxiv.
From playlist James Maynard on Numberphile
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
Lecture 23: The Dirichlet Problem on an Interval
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=QTg7040uSc0&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Kannan Soundararajan - 3/4 L-function
Kannan Soundararajan - L-function
From playlist École d'été 2014 - Théorie analytique des nombres
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
Dynamical Questions Arising from Dirichlet’s Theorem on Diophantine by Anurag Rao
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 2
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation