LATTICES WITH MANY BORCHERDS PRODUCTS

被引：13

作者：

Bruinier, Jan Hendrik ^{[1
]}

Ehlen, Stephan ^{[1
]}

Freitag, Eberhard ^{[2
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

[2] Heidelberg Univ, Math Inst, Neuenheimer Feld 288, D-69120 Heidelberg, Germany

来源：

MATHEMATICS OF COMPUTATION | 2016年 / 85卷 / 300期

基金：

美国国家科学基金会;

关键词：

EISENSTEIN SERIES; ORTHOGONAL GROUPS; REPRESENTATIONS; FORMS;

D O I：

10.1090/mcom/3059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that there are only finitely many isometry classes of even lattices L of signature (2, n) for which the space of cusp forms of weight 1 + n/2 for the Weil representation of the discriminant group of L is trivial. We compute the list of these lattices. They have the property that every Heegner divisor for the orthogonal group of L can be realized as the divisor of a Borcherds product. We obtain similar classification results in greater generality for finite quadratic modules.

引用

页码：1953 / 1981

页数：29

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