Hilbert modular forms from definite orthogonal modular forms

Abstract: In this talk, we explicitly determine the relationship between Hilbert modular forms and positive-definite orthogonal modular forms, with precise level structure and weight. This is achieved by analyzing the interaction of the even Clifford functor with the p-neighbor relation on lattices. By connecting our results to the theory of theta correspondence, we present an application to the non-vanishing of theta maps. This is joint work with Dan Fretwell, Colin Ingalls, Adam Logan, Spencer Secord and John Voight.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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