题目：Some mysteries concerning zeta functions

报告人：Marc HINDRY, Université Paris Cité（巴黎西岱大学）

时间：2024年10月23日（周三）16：00-17：00

地点：第五教学楼5207

摘要：

The mother of all zeta functions (the « s » will be important in the talk) is the well-known Euler-Riemann function. Euler calculated some of its special values, while showing a beautiful formula, which we call today Euler product formula; Riemann extended the function to the whole complex plane and showed how the prime number theorem should follow, leaving aside the famous «Riemann hypothesis».

Many generalisations have been introduced, connected with algebraic number theory, and algebraic geometry, focusing on both sides: special values and analytic properties.

I will describe precisely the main known features of Riemann’s complex zeta function and how they generalise - sometimes only conjecturally - to other zeta functions, in particular the L-function of an elliptic curve.