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
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
Mark Pollicott - Dynamical Zeta functions (Part 2)
Dynamical Zeta functions (Part 1) Licence: CC BY NC-ND 4.0
From playlist École d’été 2013 - Théorie des nombres et dynamique
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
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
Maciej Zworski - From redshift effect to classical dynamics : microlocal proof of Smale's conjecture
Dynamical zeta functions of Selberg, Smale and Ruelle are analogous to the Riemann zeta function with the product over primes replaced by products over closed orbits of Anosov flows. In 1967 Smale conjectured that these zeta functions should be meromorphic but admitted "that a positive ans
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Semyon Dyatlov: A microlocal toolbox for hyperbolic dynamics
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 Geometry
Galois theory for Schrier graphs: bounded automata by Hemant Bhate
PROGRAM DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for W
From playlist Dynamics of Complex systems 2018
Mark Pollicott - Dynamical Zeta functions (Part 3)
Dynamical Zeta functions (Part 1) Licence: CC BY NC-ND 4.0
From playlist École d’été 2013 - Théorie des nombres et dynamique
Ruelle resonances for pseudo-Anosov maps – Sébastien Gouëzel – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.6 Ruelle resonances for pseudo-Anosov maps Sébastien Gouëzel Abstract: The Ruelle resonances of a dynamical system are spectral characteristics of a system, describing the precise asymptotics of correlations. While t
From playlist Dynamical Systems and ODE
Colloquium MathAlp 2017 - Maciej Zworski
Fractal uncertainty for transfer operators I will present a new explanation of the connection between the fractal uncertainty principle (FUP) of Bourgain-Dyatlov, a statement in harmonic analysis, and the existence of zero free strips for Selberg zeta functions, which is a statement in g
From playlist Colloquiums MathAlp
Etale Theta - part 3.1 - The Groupy Definition of Xu
Here we give an alternative description of the ZZ/l cover of the punctured elliptic curve X. Twitter: @DupuyTaylor
From playlist Etale Theta
Interview at Cirm: Mark Pollicott
Interview realized during the 'Thematic Month on Dynamical Systems and Interactions' at Cirm, organized by Nicolas Bédaride (Aix-Marseille Université), Julien Cassaigne (Aix-Marseille Université), Pascal Hubert (Aix-Marseille Université). Captation: 23 February 2017 Mark Pollicott (bor
From playlist English interviews - Interviews en anglais
Hans Henrik RUGH - The Milnor-Thurston determinant and the Ruelle transfer operator
The topological entropy htop of a continuous piecewise monotone interval map measures the exponential growth in the number of monotonicity intervals for iterates of the map. Milnor and Thurston showed that exp(-htop) is the smallest zero of an analytic function, now coined the Milnor-Thurs
From playlist Ruelle-Fest : avancées récentes en théorie des systèmes dynamiques
Interview at Cirm : David Ruelle
David Ruelle est professeur honoraire de Physique Théorique à l’Institut des Hautes Études Scientifiques (IHÉS). http://www.ihes.fr/~ruelle/ Son parcours professionnel • 1955 : diplômes de : candidat ingénieur civil de la Faculté polytechnique de Mons. candidat en sciences mathématiqu
From playlist Mathematical Physics
Frédéric Faure: Emergence of the quantum wave equation in classical deterministic...
In the 80’s, D. Ruelle, D. Bowen and others have introduced probabilistic and spectral methods in order to study deterministic chaos (”Ruelle resonances”). For a geodesic flow on a strictly negative curvature Riemannian manifold, following this approach and use of microlocal analysis, one
From playlist Analysis and its Applications
Mémoires de David Ruelle, entretien du 2 avril 2015 - The Golden Years of the IHES
Questions 0:24 You are David Ruelle, a mathematical physicist, and you joined IHES in 1964. Could you explain why you chose to come here? 2:59 You want to talk about the Golden Period at the Institut des Hautes Etudes Scientiques. Have you known other golden periods at other places? 6:12 W
From playlist Les entretiens de l'IHES
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