Particular values of Riemann zeta function

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Particular values of Riemann zeta function
제안자 안흥주
자문교원 안흥주, 이두석
연도 2020
타입 A형 과제
코스 프란시스 크릭
매칭여부 Yes
참여학생수 4

제안 배경

This is a continued project starting at 2019. Everyone interested in this topic is welcome to join, even though this project is targeted for the math oriented students.

Riemann zeta function is a complex valued function (the Dirichlet series $\zeta(s)=\sum_{n=1}^\infty {1}/{n^s}$) of a complex variable $s$ that is extended analytically to the whole plane except to the point $s=1+0\sqrt{-1}$. The values of the Riemann zeta function at $s=2n$, $n=1,2,3,\dots$ were computed by Euler and the values at negative integer points also found by Euler are rational numbers. In 1979 Roger Apéry and his successors proved the irrationality of $\zeta(3)$. Next, the proof of the irrationality of $\zeta(5)$ is waiting to be attacked.

과제 목표

Prove that $\zeta(5)$ is irrational. Of course, there is a possibility that $\zeta(5)$ is a rational number. Who knows?

과제 내용

  • Basic Study of the representations of $\zeta$
  • Reviews of the irrationality proofs of other mathematical constants
  • Study of the importance of the zeta function
  • How to edit a mathematical writing
  • Etc