Algebra of Borcherds products
Number Theory
2021-05-25 v3 Algebraic Geometry
Rings and Algebras
Representation Theory
Abstract
Borcherds lift for an even lattice of signature (p,q) is a lifting from weakly holomorphic modular forms of weight (p-q)/2 for the Weil representation. We introduce a new product operation on the space of such modular forms and develop a basic theory. The product makes this space a finitely generated filtered associative algebra, without unit element and noncommutative in general. This is functorial with respect to embedding of lattices by the quasi-pullback. Moreover, the rational space of modular forms with rational principal part is closed under this product. In some examples with p=2, the multiplicative group of Borcherds products of integral weight forms a subring.
Cite
@article{arxiv.2007.09918,
title = {Algebra of Borcherds products},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:2007.09918},
year = {2021}
}