Zeta functions of certain 2-parameter families of $K3$ surfaces via the Appell functions
| 구분 | 정수론,학부생,학생(팀) |
|---|---|
| 일정 | 2025-10-17(금) 11:00~12:00 |
| 세미나실 | 27동 325호 |
| 강연자 | Kumabe Satoshi (Kyushu University) |
| 담당교수 | 김도형 |
| 기타 |
정수론세미나
일시: 10월17일(금) 11시-12시
장소: 27-325
Speaker: Kumabe Satoshi(Kyushu)
Title: Zeta functions of certain 2-parameter families of $K3$ surfaces via the Appell functions
Abstract:
The hypergeometric functions are given as complex power series with parameters. On the other hand, analogous functions, called hypergeometric functions over finite fields, are defined as functions on finite fields with multiplicative characters as parameters. In the first part of this talk, we will review the definitions and fundamental properties of hypergeometric functions over finite fields. After that, we apply them to describe the zeta functions of algebraic varieties over finite fields. In particular, we explain that the zeta functions of certain 2-parameter families of $K3$ surfaces can be described by the roots of the zeta functions of the two Legendre elliptic curves.
