Title: Modularity in Genus Two
Speaker: David Yuen
Speaker Info: Lake Forest College
Brief Description:
Special Note:
Abstract:
Modularity in genus one invovles weight two elliptic modular forms. Modularity in genus two invovles weight two Siegel paramodular forms. We consider several ways of computing Siegel modular forms over the paramodular group K(N) in genus two. We compile, in conjunction with A. Brumer and K. Kramer's data on abelian surfaces, substantial evidence for the Paramodular Conjecture. We gain strong evidence for existence and nonexistence of nonlift paramodular eigenforms of weight two for general levels N < 1000. We will show how to construct, using the method of integral closure, a nonlift paramodular eigenform of level 277 that should correspond to the abelian surface of conductor 277; and how to construct, using a Borcherds product, a nonlift paramodular eigenform of level 587 that should correspond to the abelian surface of conductor 58.Date: Monday, October 07, 2013