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arXiv · 2007.09918

Algebra of Borcherds products

Shouhei Ma
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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.

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Shouhei Ma. 2020-07-20. Algebra of Borcherds products. https://arxiv.org/abs/2007.09918

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