Open Access
October 2016 The representation function for sums of three squares along arithmetic progressions
Paul Pollack
Proc. Japan Acad. Ser. A Math. Sci. 92(8): 96-99 (October 2016). DOI: 10.3792/pjaa.92.96

Abstract

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.

Citation

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Paul Pollack. "The representation function for sums of three squares along arithmetic progressions." Proc. Japan Acad. Ser. A Math. Sci. 92 (8) 96 - 99, October 2016. https://doi.org/10.3792/pjaa.92.96

Information

Published: October 2016
First available in Project Euclid: 3 October 2016

zbMATH: 06673661
MathSciNet: MR3554863
Digital Object Identifier: 10.3792/pjaa.92.96

Subjects:
Primary: 11R11 , 11R29
Secondary: 11E25

Keywords: Class number , imaginary quadratic field , three squares

Rights: Copyright © 2016 The Japan Academy

Vol.92 • No. 8 • October 2016
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