Maass relations for Saito-Kurokawa lifts of higher levels

Abstract: It is known that a Siegel modular form is a (classical) Saito-Kurokawa lift of an elliptic modular form if and only if its Fourier coefficients satisfy the so-called Maass relations. The first construction of such a lift was given by Maass using correspondences between various modular forms. However, in order to generalize this lift to higher levels it is easier to use a construction coming from representation theory. During the talk we present history of this problem and briefly discuss the aforementioned constructions. We also indicate how one can read off the Maass relations from the latter. This work generalizes an approach of Pitale, Saha and Schmidt from the classical to a higher level case.

number theory

Audience: researchers in the topic

( slides )

Warsaw Number Theory Seminar