Hilbert modular forms obtained from orthogonal modular forms on quaternary lattices

Abstract: We make explicit the relationship between Hilbert modular forms and orthogonal modular forms arising from positive definite quaternary lattices over the ring of integers of a totally real number field. Our work uses the Clifford algebra, and it generalizes that of Ponomarev, Bocherer--Schulze-Pillot, and others by allowing for general discriminant, weight, and class group of the base ring. This is joint work with Eran Assaf, Dan Fretwell, Colin Ingalls, Adam Logan, and Spencer Secord.

number theory

Audience: researchers in the topic

Comments: pre-talk at 3pm

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.