Antisymmetric Paramodular Forms of Weights 2 and 3
Number Theory
2016-09-15 v1
Abstract
We define an algebraic set in ~dimensional projective space whose -rational points correspond to meromorphic, antisymmetric, paramodular Borcherds products. We know two lines inside this algebraic set. Some rational points on these lines give holomorphic Borcherds products and thus construct examples of Siegel modular forms on degree two paramodular groups. Weight examples provide antisymmetric canonical differential forms on Siegel modular threefolds. Weight is the minimal weight and these examples, via the Paramodular Conjecture, give evidence for the modularity of some rank one abelian surfaces defined over .
Cite
@article{arxiv.1609.04146,
title = {Antisymmetric Paramodular Forms of Weights 2 and 3},
author = {Cris Poor and Valery Gritsenko and David S. Yuen},
journal= {arXiv preprint arXiv:1609.04146},
year = {2016}
}