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Small Positive Values of Indefinite Quadratic Forms

Published online by Cambridge University Press:  20 November 2018

J. H. H. Chalk
J. H. H. Chalk*
Affiliation:
University of Toronto
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Let ∧ denote the lattice of points X = (x1, …, xn) with integral coordinates. A basis of ∧ is a set of n points X1, …, Xn of ∧ such that every point of ∧ is expressible in the form where ui are integers. It is easy to see that points X1, …, Xn of ∧ form a basis if, and only if

(1)

where Xr = (x1(r), …, x1(r)).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 3 , 01 September 1963 , pp. 331 - 339
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Chalk, J. H. H., Integral Bases for Quadratic Forms, Canadian J. of Mathematics, 15(1963), 412-421.Google Scholar
2. Davenport, H. and Ridout, D., Indefinite Quadratic Forms, Proc. London Math. Soc., (3), 9(1959), 544-555.Google Scholar
3. Foster, D. M. E., Indefinite Quadratic Polynomials innvariables, Mathematika, 3 (1956), 111-116, Theorem 2.Google Scholar
4. Watson, G. L., Distinct small values of Quadratic Forms, Mathematika, 7 (1960), 36-40, Theorem 1.Google Scholar