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Zhilin Luo : Bias of root numbers for Hilbert new forms of cubic level (Nov 3, 2021 3:10 PM)
We express the bias of global root numbers of Hilbert new forms of cubic level via special values of Dedekind L-functions attached to CM extensions determined by the level. In particular, our formula includes the case when weight 2 appears. We establish the formula by 1) a limit form of Jacquet-Zagier trace formula on PGL_2 associated to certain not necessarily integrable test functions at Archimedean places (when weight 2 occurs), and 2) showing the meromorphic continuation of certain Dirichlet series with coefficients given by special value of Dedekind L-functions via spectral side of the Jacquet-Zagier trace formula. This is a joint work with Q. Pi and H. Wu. arXiv: 2110.08310.
- Category: Number Theory
- Duration: 01:34:39
- Date: November 3, 2021 at 3:10 PM
- Views: 198
- Tags: seminar, Number Theory Seminar
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