On representation of an integer as the sum of three squares and ternary quadratic forms with the discriminants p2, 16p2

JOURNAL OF NUMBER THEORY

卷:132

Article

Berkovich, Alexander¹  Jagy, William C.² 

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[2] Math Sci Res Inst, Berkeley, CA 94720 USA

关键词: Ternary quadratic forms;    Sum of three squares;    Local densities;    Siegel-Weil formula;    Smith-Minkowski mass formula;    theta-function identities;    Watson's m-map;   

DOI  :  10.1016/j.jnt.2011.09.001

来源: Elsevier

【 摘 要 】

Let s(n) be the number of representations of n as the sum of three squares. We prove a remarkable new identity for s(p(2)n) - ps(n) with p being an odd prime. This identity makes nontrivial use of ternary quadratic forms with discriminants p(2), 16p(2). These forms are related by Watson's transformations. To prove this identity we employ the Siegel-Weil and the Smith-Minkowski product formulas. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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