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Sums of squares of integral linear forms

Part of: Basic linear algebra Forms and linear algebraic groups

Published online by Cambridge University Press:  09 April 2009

Hideyo Sasaki
Hideyo Sasaki
Affiliation:
The Graduate School of Science and Technology Kobe University1-1 Rokkodai-cho Nada-ku Kobe 657-8501Japan e-mail: hsasaki@math.kobe-u.ac.jp
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Abstract

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In 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.

MSC classification

Secondary: 11E08: Quadratic forms over local rings and fields 11E12: Quadratic forms over global rings and fields 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 11E25: Sums of squares and representations by other particular quadratic forms 15A63: Quadratic and bilinear forms, inner products
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 298 - 302
Copyright
Copyright © Australian Mathematical Society 2000

References

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