Arithmetic Geometry and Number Theory Seminar: Birch and Swinnerton-Dyer Formula for modular forms of arbitrary weight in the cases of analytic ranks 0 and 1

Seminar | December 10 | 3:10-4 p.m. | 891 Evans Hall

 Dimitar Jetchev, EPFL and Inpher, Inc.

 Department of Mathematics

I will report on recent results on the computation of the $p$-part of the leading term of the $L$-function of a modular form of arbitrary weight at the central point in the cases when the order of vanishing is at most 1. Unlike the classical case of weight 2 modular forms, qualitatively different arguments are needed in the higher-weight case. After explaining the difference, I will indicate how one can use level-raising and (non-ordinary) $p$-adic deformations together with some of the arguments in weight 2 to obtain results in the case of general weights.

This is joint work with Chris Skinner and Xin Wan.