Siegel modular forms of genus 2 with the simplest divisor

被引：25

作者：

Clery, F. ^{[1
]}

Gritsenko, V. ^{[2
]}

机构：

[1] Univ Amsterdam, FNWI, Korteweg de Vries Inst Wiskunde, NL-1090 GE Amsterdam, Netherlands

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2011年 / 102卷

关键词：

AUTOMORPHIC-FORMS;

D O I：

10.1112/plms/pdq036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exist exactly eight Siegel modular forms with respect to the congruence subgroups of Hecke type of the paramodular groups of genus 2 vanishing precisely along the diagonal of the Siegel upper half-plane. This is a solution of a question formulated during the conference 'Black holes, Black Rings and Modular Forms' (ENS, Paris, August 2007). These modular forms generalize the classical Igusa form and the forms constructed by Gritsenko and Nikulin in 1998.

引用

页码：1024 / 1052

页数：29

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