# Particular values of Riemann zeta function

Particular values of Riemann zeta function | |
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제안자 | 안흥주 |

자문교원 | 안흥주, 이두석 |

연도 | 2020 |

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)