Text only print
Full screen print
Number Theory Seminar
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| 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)
https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html
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 ]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.
https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html
