论文标题
Borcherds产品代数
Algebra of Borcherds products
论文作者
论文摘要
Borcherds升起的均匀签名晶格（P，Q）是从弱塑形模块化形式的重量（P-Q）/2的提升。我们在这种模块化形式的空间上介绍了一个新产品操作，并发展了基本理论。该产品使该空间成为有限生成的过滤联想代数，而没有单位元素，并且通常是非交通性的。这是关于准扣子嵌入晶格的功能。此外，在该产品下，模块化形式具有理性主部分的理性空间是关闭的。在某些p = 2的示例中，整体权重的繁殖力组产物形成了一个子。
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.
