Sums of five, seven and nine squares

被引：28

作者：

Cooper, S ^{[1
]}

机构：

[1] Massey Univ Albany, Inst Informat & Math Sci, Auckland, New Zealand

来源：

RAMANUJAN JOURNAL | 2002年 / 6卷 / 04期

关键词：

Hecke operator; modular forms of half integer weight; sums of squares;

D O I：

10.1023/A:1021175617574

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let r(k)(n) denote the number of representations of an integer n as a sum of k squares. We prove that [GRAPHICS] where [GRAPHICS] Here n = 2(lambda)Pi(p) p(lambdap) is the prime factorisation of n, n' is the square-free part of n, the products are taken over the odd primes p, and (n/p) is the Legendre symbol. Some similar formulas for r(7)(n) and r(9)(n) are also proved.

引用

页码：469 / 490

页数：22

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