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1 November 2006 Estimates for representation numbers of quadratic forms
Valentin Blomer, Andrew Granville
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Duke Math. J. 135(2): 261-302 (1 November 2006). DOI: 10.1215/S0012-7094-06-13522-6

Abstract

Let f be a primitive positive integral binary quadratic form of discriminant D, and let rf(n) be the number of representations of n by f up to automorphisms of f. In this article, we give estimates and asymptotics for the quantity nxrf(n)β for all β0 and uniformly in D=o(x). As a consequence, we get more-precise estimates for the number of integers which can be written as the sum of two powerful numbers

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Valentin Blomer. Andrew Granville. "Estimates for representation numbers of quadratic forms." Duke Math. J. 135 (2) 261 - 302, 1 November 2006. https://doi.org/10.1215/S0012-7094-06-13522-6

Information

Published: 1 November 2006
First available in Project Euclid: 17 October 2006

zbMATH: 1135.11020
MathSciNet: MR2267284
Digital Object Identifier: 10.1215/S0012-7094-06-13522-6

Subjects:
Primary: 11E16
Secondary: 11N56

Rights: Copyright © 2006 Duke University Press

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Vol.135 • No. 2 • 1 November 2006
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