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Philadelphia Area Number Theory Seminar

Wednesday, April 12, 2017 - 2:30pm

Dianbin Bao

Temple University


Bryn Mawr College

Park 328

This talk will focus on polynomial identities between Hecke eigenforms. In particular we will show that assuming Maeda's conjecture, then all solutions to the equation X^2=\sum a_iY_i in terms of Hecke eigenforms for SL_2(Z) are forced by dimension considerations. Our proof uses Galois theory for the eigenvalues of the Hecke operators acting the space of cusp forms for SL_2(Z). We will also talk about how this is related with nonvanishing of certain L-series and the case for the congruence subgroups.