Lecture

Stirling's Formula and Functional Equation for Zeta

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-313: Number theory I.b - Analytic number theory

The aim of this course is to present the basic techniques of analytic number theory. ...

Description

This lecture covers the proof of Stirling's asymptotic formula for the Gamma function and the halfway proof of the functional equation of the Zeta function, discussing the implications and applications of these results in mathematical analysis.

Official source

Ontological neighbourhood

Mathematics

Analysis: Complex analysis

Related concepts (32)

Role-playing

Role-playing or roleplaying is the changing of one's behaviour to assume a role, either unconsciously to fill a social role, or consciously to act out an adopted role. While the Oxford English Dictionary offers a definition of role-playing as "the changing of one's behaviour to fulfill a social role", in the field of psychology, the term is used more loosely in four senses: To refer to the playing of roles generally such as in a theatre, or educational setting; To refer to taking a role of a character or person and acting it out with a partner taking someone else's role, often involving different genres of practice; To refer to a wide range of games including role-playing video game (RPG), play-by-mail games and more; To refer specifically to role-playing games.

Role-playing game

A role-playing game (sometimes spelled roleplaying game, RPG) is a game in which players assume the roles of characters in a fictional setting. Players take responsibility for acting out these roles within a narrative, either through literal acting or through a process of structured decision-making regarding character development. Actions taken within many games succeed or fail according to a formal system of rules and guidelines. There are several forms of role-playing games.

Role-playing video game

A role-playing video game, commonly referred to as a role-playing game (RPG) or computer role-playing game (CRPG), is a video game genre where the player controls the actions of a character (or several party members) immersed in some well-defined world, usually involving some form of character development by way of recording statistics. Many role-playing video games have origins in tabletop role-playing games and use much of the same , settings and game mechanics.

Tactical role-playing game

Tactical role-playing games (abbreviated TRPGs), also known as strategy role-playing games and in Japan as simulation RPGs (both abbreviated SRPGs), are a video game genre that combines core elements of role-playing video games with those of tactical (turn-based or real-time) strategy video games. The formats of tactical RPGs are much like traditional tabletop role-playing games and strategy games in appearance, pacing, and rule structure.

Data Encryption Standard

The Data Encryption Standard (DES ˌdiːˌiːˈɛs,_dɛz) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cryptography. Developed in the early 1970s at IBM and based on an earlier design by Horst Feistel, the algorithm was submitted to the National Bureau of Standards (NBS) following the agency's invitation to propose a candidate for the protection of sensitive, unclassified electronic government data.

Related lectures (64)

Functional Equation of Zeta and Hadamard Products

Covers the functional equation of the Zeta function and the Hadamard factorization theorem.

Non-vanishing of Dirichlet L-function and Gamma functions

Covers the proof of non-vanishing of Quadratic Dirichlet L-function and reviews basic properties of Gamma function.

Analytical Extension of Gamma Function

Covers the analytical extension of the Gamma function to real and complex numbers, discussing properties and convergence.

Hadamard Factorization and Zeros of Zeta

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

Riemann Zeta Function