Monthly Seminar on Arithmetic of Automorphic Forms

Seminar information archive ~04/21Next seminarFuture seminars 04/22~

Date, time & place Saturday 13:30 - 16:00 123Room #123 (Graduate School of Math. Sci. Bldg.)

2013/06/22

10:00-12:15   Room #123 (Graduate School of Math. Sci. Bldg.)
Kei-ichi Gunji (Chiba Inst. Tech) 10:00-11:00
On the computation of the ramified Siegel series associated with
trivial character (JAPANESE)
[ Abstract ]
Please check the Japanese version of the web page.
Masao Tsuzuki (Sophia University) 11:15-12:15
An explicit relative trace formula for Hilbert modular forms and its applications
(JAPANESE)
[ Abstract ]
This is joint work with Shingo Sugiyama. In this talk, we report our recent result on relative trace formula on PGL(2) computing the spectral averages for the central L-values of quadratic base change of holomorphic Hilbert mudular forms. explicitly all local terms of the trace formula, dropping several assumptions which have always been assumed in existing works of similar theme. The following applications of our explicit relative trace formula will be explained:
(i) a spectral equidistribution result in the leve aspect for the Satake parameters weighted by central L-values;
(ii) a subconvexity bound of quadratic base change L-functions for holomorphic Hilbert cusp forms in the weight aspect;
(iii) Existence of infinitely many holomorphic Hilbert cusp forms with arbitrarily large field of definition and with non vanishing central $L$-values.