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Integral Bases for Quadratic Forms

Published online by Cambridge University Press:  20 November 2018

J. H. H. Chalk
J. H. H. Chalk*
Affiliation:
University of Toronto and University College, London
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Let

be an indefinite quadratic form in the integer variables x1, . . . , xn with real coefficients of determinant D = ||ars||(n) ≠ 0. The homogeneous minimum MH(Qn) and the inhomogeneous minimum MI(Qn) of Qn(x) are defined as follows :

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 412 - 421
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Birch, B. J., The inhomogeneous minimum of quadratic forms of signature zero, Acta Arith., 4 (1957), 85–98.Google Scholar
2. Blaney, H., Indefinite quadratic forms in n variables, J. London Math. Soc, 23 (1948), 153–160.Google Scholar
3. Davenport, H., Indefinite quadratic forms in many variables, Mathematika, 3 (1956); 8 1 - 101; see also D. Ridout, 5 (1958), 122–124, for references and later work.Google Scholar
4. Davenport, H., Non-homogeneous ternary quadratic forms, Acta Math., 80 (1948), 65–95.Google Scholar
5. E, D. M.. Foster, in preparation.Google Scholar
6. Oppenheim, A., Value of quadratic forms I, Quart. J. Math. Oxford (2), 4 (1953), 54–59.Google Scholar
7. Oppenheim, A., Value of quadratic forms III, Monats. Math., 57 (1953), 97–101.Google Scholar
8. Watson, G. L., Distinct small values of quadratic forms, Mathematika, 7 (1960), 36–40.Google Scholar
9. Watson, G. L., Indefinite quadratic polynomials, Mathematika, 7 (1960), 141–144.Google Scholar