Particular values of Riemann zeta function
| Particular values of Riemann zeta function | |
|---|---|
| 제안자 | 안흥주 |
| 자문교원 | 안흥주, 이두석 |
| 연도 | 2020 |
| 분류 | |
| 타입 | A형 과제 |
| 코스 | 프란시스 크릭 |
| 매칭여부 | Yes |
| 참여학생수 | 4 |
| 소개동영상 | |
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
참고자료
- http://mathworld.wolfram.com/RiemannZetaFunction.html
- Many odd zeta values are irrational
- One of the Odd Zeta Values from ζ(5) to ζ(25) Is Irrational. By Elementary Means
- ζ(5) is irrational (wrong proof)
