10 novembre 2020

Abhishek Saha (Queen Mary University of London)
Critical L-values and congruence primes for Siegel modular forms

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Lieu : Séminaire en ligne

Résumé : I will explain some recent joint work with Pitale and
Schmidt where we obtain an explicit integral representation for the
L-function on GSp_2n \times GL_1 associated to a
holomorphic vector-valued Siegel cusp form of degree n and arbitrary
level, and a Dirichlet character. By combining this integral
representation with a detailed arithmetic study of nearly holomorphic
Siegel cusp forms (joint with Pitale, Schmidt, and Horinaga) we are
able to prove an algebraicity result for the critical L-values on
GSp_2n \times GL_1. To refine this result further, we prove that the
pullback of the nearly holomorphic Eisenstein series that appears in
our integral representation is actually cuspidal in each variable and
has nice p-adic arithmetic properties. This leads to a result
on congruences between Hecke eigenvalues of two Siegel cusp forms of
degree 2 modulo primes dividing a certain quotient of L-values.

Critical L-values and congruence primes for Siegel modular forms  Version PDF