Number Theory Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Naoki Imai, Shane Kelly

2020/05/27

17:30-18:30   Online
Kenichi Bannai (Keio University/RIKEN)
Shintani generating class and the p-adic polylogarithm for totally real fields (ENGLISH)
[ Abstract ]
In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke $L$-functions for totally real fields. In particular, we will construct a canonical class, which we call the Shintani generating class, in the cohomology of a certain quotient stack of an infinite direct sum of algebraic tori associated with a fixed totally real field. Using our observation that cohomology classes, not functions, play an important role in the higher dimensional case, we proceed to newly define the p-adic polylogarithm function in this case, and investigate its relation to the special value of p-adic Hecke $L$-functions. Some observations concerning the quotient stack will also be discussed. This is a joint work with Kei Hagihara, Kazuki Yamada, and Shuji Yamamoto.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html