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arXiv:1101.2951 [math.NT]AbstractReferencesReviewsResources

On representation of an integer as the sum of three squares and the ternary quadratic forms with the discriminants p^2, 16p^2

Alexander Berkovich, Will Jagy

Published 2011-01-15, updated 2011-01-30Version 2

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^2n)- ps(n) with p being an odd prime. This identity makes nontrivial use of ternary quadratic forms with discriminants p^2 and 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.

Comments: 17 pages
Categories: math.NT, math.CO
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