Theta integrals and Siegel Eisenstein series of low weight

Speaker's Name: Jens Funke
Speaker's Affiliation: Durham University
Speaker's Research Theme(s): Pure Mathematics
Abstract:
Eisenstein series are a critical component in the theory of modular forms. In the elliptic case, we easily construct holomorphic forms in weights larger than 2, whereas Hecke summation can yield non-holomorphic forms for the low weights 3/2 and 2. On the other hand, the Siegel-Weil formula relates (integrals of) theta series associated to orthogonal groups to Siegel Eisenstein series. In the positive definite case one obtains holomorphic forms but for indefinite quadratic forms the situation is considerably more complicated. In this talk, we give an introduction to the problem and then discuss theta lifts for signature (n,2) to Siegel modular forms of degree n and weight (n+1)/2 from both a geometric and a modular perspective. This is joint work in progress with J Bruinier, P Kiefer, E. Rosu.

Venue: Maths A17