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

共 28 条

[11]

Ehlen S., 2014, FINITE QUADRATIC MOD

[12]

Fischer J., 1987, LECT NOTES MATH, V1253

[13]

Freitag E., 2014, RIEMANN SURFACES

[14]

Hagemeier H., 2010, THESIS TU DARMSTADT

[15]

Kitaoka Y., 1993, CAMBRIDGE TRACTS MAT, V106

[16] Eisenstein series for SL(2) [J].

Kudla, Stephen S. ;

Yang TongHai .

SCIENCE CHINA-MATHEMATICS, 2010, 53 (09) :2275-2316

[17]

Nikulin VV., 1979, Izv. Akad. Nauk SSSR Ser. Mat, V43, P111

[18] IRREDUCIBLE REPRESENTATIONS OF GROUPS SL2(ZP), ESPECIALLY SL2(Z2) .1. [J].

NOBS, A .

COMMENTARII MATHEMATICI HELVETICI, 1976, 51 (04) :465-489

[19] SOME CONSTRUCTIONS OF MODULAR FORMS FOR THE WEIL REPRESENTATION OF SL2(Z) [J].

Scheithauer, Nils R. .

NAGOYA MATHEMATICAL JOURNAL, 2015, 220 :1-43

[20] On the classification of automorphic products and generalized Kac-Moody algebras [J].

Scheithauer, NR .

INVENTIONES MATHEMATICAE, 2006, 164 (03) :641-678

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