The Ramanujan conjecture for Bianchi modular forms and the Dwork family

James Newton (University of Oxford)

Wednesday 18th February 16:00-17:00
Maths 311B

Abstract

I'll talk about joint work with George Boxer, Frank Calegari, Toby Gee and Jack Thorne from a couple of years ago, in which we prove some well-known conjectures (Ramanujan and Sato--Tate) for Bianchi modular forms. (Shortly after our work appeared, Kojiro Matsumoto proved more general results of this type.) In this talk, one ingredient I would like to say something about is an application to the Dwork family of projective hypersurfaces of a result of Drinfeld and Kedlaya on p-adic valuations of Frobenius eigenvalues.

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