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Sums of squares of integral linear forms

Sums of squares of integral linear forms AbstractIn this paper we prove that every positive definite n-ary integral quadratic form with 12 < n < 13 (respectively 14 ≦ n ≤ 20) that can be represented by a sum of squares of integral linear forms is represented by a sum of 2 · 3n + n + 6 (respectively 3 · 4n + n + 3) squares. We also prove that every positive definite 7-ary integral quadratic form that can be represented by a sum of squares is represented by a sum of 25 squares. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics Cambridge University Press

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Publisher
Cambridge University Press
Copyright
Copyright © Australian Mathematical Society 2000
ISSN
0263-6115
DOI
10.1017/S1446788700002470
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper we prove that every positive definite n-ary integral quadratic form with 12 < n < 13 (respectively 14 ≦ n ≤ 20) that can be represented by a sum of squares of integral linear forms is represented by a sum of 2 · 3n + n + 6 (respectively 3 · 4n + n + 3) squares. We also prove that every positive definite 7-ary integral quadratic form that can be represented by a sum of squares is represented by a sum of 25 squares.

Journal

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and StatisticsCambridge University Press

Published: Apr 9, 2009

Keywords: primary 11E08; 11E12; 11E20; 11E25; 15A63

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