Inhomogeneous quadratic forms and triangular numbers

被引：11

作者：

Shimura, G ^{[1
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2004年 / 126卷 / 01期

关键词：

D O I：

10.1353/ajm.2004.0007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove an explicit formula for the number of representations of an integer as the sum of n triangular numbers for each n in the range 2 less than or equal to n less than or equal to 8 as special cases of a more general formula applicable to an inhomogeneous quadratic form over a totally real number field. The formula can be derived by calculating explicitly the Fourier coefficients of a certain Eisenstein series that appears in the Siegel-Weil formula for an inhomogeneous quadratic form.

引用

页码：191 / 214

页数：24

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