The representation function for sums of three squares along arithmetic progressions

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Paul Pollack¹ 

[1] Department of Mathematics, University of Georgia, Boyd Graduate Studies Research Center

关键词: Class number;    imaginary quadratic field;    three squares.;   

DOI  :  10.3792/pjaa.92.96

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

For positive integers $n$, let $r(n) = \#\{(x,y,z) \in\mathbf{Z}^{3}: x^{2}+y^{2}+z^{2}=n\}$. Let $g$ be a positive integer, and let $A\bmod{M}$ be any congruence class containing a squarefree integer. We show that there are infinitely many squarefree positive integers $n\equiv A\bmod{M}$ for which $g$ divides $r(n)$. This generalizes a result of Cho.

【 授权许可】

Unknown