Orthogonal modular forms from definite quaternary lattices

Abstract: In this talk I will make precise the fact that definite quaternary orthogonal modular forms are Hilbert modular forms. By taking the algebraic approach and using the Clifford functor, we can avoid analytic difficulties in the theta lifts, and give a precise description of level and character on both sides of the transfer map. Building on advancements in our understanding of orders in quaternion algebras, we are able to apply this result to a large class of lattices, allowing for singularities of high codimension. This is joint work with Dan Fretwell, Adam Logan, Colin Ingalls, Spencer Secord and John Voight.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar