Simple graded rings of Siegel modular forms, differential operators and Borcherds products

被引：69

作者：

Aoki, H ^{[1
]}

Ibukiyama, T

机构：

[1] Sci Univ Tokyo, Fac Sci & Technol, Dept Math, Noda, Chiba 2788510, Japan

[2] Osaka Univ, Dept Math, Grad Sch Sci, Toyonaka, Osaka 5600043, Japan

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2005年 / 16卷 / 03期

关键词：

Siegel modular form; differential operator; Borcherds product;

D O I：

10.1142/S0129167X05002837

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that the graded ring of Siegel modular forms of Gamma(0) (N) subset of Sp(2, Z) has a very simple unified structure for N = 1, 2, 3, 4, taking Neben-type case (the case with character) for N = 3 and 4. All are generated by 5 generators, and all the fifth generators axe obtained by using the other four by means of differential operators, and it is also obtained as Borcherds products. As an appendix, examples of Euler factors of L-functions of Siegel modular forms of Sp(2, Z) of odd weight are given.

引用

页码：249 / 279

页数：31

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