Number theory seminar

March 4, 2016 @ 1:30 pm – March 4, 2016 @ 2:30 pm
Keller 402

Speaker: Jerry Shurman (Reed College)

Title: Lifts and Congruences of Siegel Modular Forms by the Pullback-Genus Method

Abstract: We compute Hecke eigenform bases of spaces of degree 3 Siegel modular forms and Euler factors of the eigenforms, through weight 22. Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known and computationally tractable, and Garrett’s decomposition of the pullback of the Eisenstein series through the Witt map. Our results support Miyawaki’s conjectural lift and Katsurada’s theory of congruence neighbors. Some familiarity with classical modular forms will be helpful.