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15 March 2009 Almost-universal quadratic forms: An effective solution of a problem of Ramanujan
J. Bochnak, B.-K. Oh
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Duke Math. J. 147(1): 131-156 (15 March 2009). DOI: 10.1215/00127094-2009-008

Abstract

In this article we investigate almost-universal positive-definite integral quaternary quadratic forms, that is, those representing sufficiently large positive integers. In particular, we provide an effective characterization of all such forms. In this way we obtain the final solution to a problem first addressed by Ramanujan in [12]. Special attention is given to 2-anisotropic almost-universal quaternaries

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J. Bochnak. B.-K. Oh. "Almost-universal quadratic forms: An effective solution of a problem of Ramanujan." Duke Math. J. 147 (1) 131 - 156, 15 March 2009. https://doi.org/10.1215/00127094-2009-008

Information

Published: 15 March 2009
First available in Project Euclid: 26 February 2009

zbMATH: 1242.11028
MathSciNet: MR2494458
Digital Object Identifier: 10.1215/00127094-2009-008

Subjects:
Primary: 11E12 , 11E20

Rights: Copyright © 2009 Duke University Press

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Vol.147 • No. 1 • 15 March 2009
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