The Arithmetic of Power Series and Applications to Period

Caltech-Tsinghua Joint Colloquium

Organizers：

Shoma Sugimoto, Song Yu, Roy Zhao

Speaker：

Yunqing Tang 唐云清

Berkeley/Caltech

Time：

Wednesday 8:00 am

Oct. 30, 2024

Venue：

C548, Shuangqing Complex Building

Online：

https://caltech.zoom.us/j/83227207916?pwd=R8hqeEwfn7jb9ZVLt4px16a2LTAU00

Title：

The Arithmetic of Power Series and Applications to Period

Abstract：

Borel and Dwork gave conditions on when a nice power series with rational number coefficients comes from a rational function in terms of meromorphic convergence radii at all places. Such a criterion was used in Dwork’s proof of the rationality of zeta functions of varieties over finite fields. Later, the work of André, Bost, Charles and many others generalized the rationality criterion of Dwork and deduced many applications in the arithmetic of differential equations and elliptic curves. In this talk, we will briefly review the history and then discuss some further refinements and generalizations of the criteria of André, Bost, and Charles and their application to irrationality of a special value of a certain Dirichlet L-function using rational approximations constructed by Zagier. This is joint work with Frank Calegari and Vesselin Dimitrov.

About the Speaker：

Yunqing Tang is a professor at Caltech and University of California, Berkeley specializing in number theory and arithmetic geometry. She received her PhD from Harvard University in 2016. Tang previously was a Member at the IAS, an Instructor at Princeton University, a junior researcher (Chargee de recherche) at CNRS/Universite Paris-Sud, and an assistant professor at Princeton University. Tang has recently been awarded a Sloan Research Fellowship, the SASTRA Ramanujan prize, and the AWM Microsoft Research Prize in Algebra and Number Theory.