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Lithuanian Mathematical Journal

, Volume 50, Issue 2, pp 140–163 | Cite as

On primitively universal quadratic forms

  • N. Budarina
Article

Abstract

In 1999, Manjul Bhargava proved the Fifteen Theorem and showed that there are exactly 204 universal positive definite integral quaternary quadratic forms. We consider primitive representations of quadratic forms and investigate a primitive counterpart to the Fifteen Theorem. In particular, we give an efficient method for deciding whether a positive definite integral quadratic form in four or more variables with odd square-free determinant is almost primitively universal.

Keywords

almost primitively universal quadratic forms p-adic symbols 

MSC

11E20 11E25 11E08 11E99 

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Logic HouseNational University of IrelandMaynoothIreland

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