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Some remarks on representations of positive definite quadratic forms

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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Let S, T be positive definite integral symmetric matrices of degree m, n respectively and let us consider the quadratic diophantine equation S[X] = T. We know already [1] that the following assertion (A)m>n is true for m ≥ 2n + 3.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 23 - 41
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[1] Hsia, J. S., Kitaoka, Y., Kneser, M., Representations of positive definite quadratic forms, J. reine angew. Math., 301 (1978), 132–141.Google Scholar
[2] Kitaoka, Y., Modular forms of degree n and representation by quadratic forms II, Nagoya Math. J., 87 (1982), 127–146.CrossRefGoogle Scholar
[3] Kitaoka, Y., Lectures on Siegel modular forms and representation by quadratic forms, Tata Institute of Fundamental Research, Bombay, Berlin-Heidelberg-New York, Springer 1986.Google Scholar
[4] Kitaoka, Y., Local densities of quadratic forms, In: Investigations in Number Theory, 1987 (Advanced Studies in Pure Math. 13, pp. 433–460).Google Scholar
[5] Kitaoka, Y., A note on representation for positive definite binary quadratic forms by positive definite quadratic forms in 6 variables, to appear,Google Scholar
[6] Kitaoka, Y., Modular forms of degree n and representation by quadratic forms V, Nagoya Math. J., 111 (1988), 173–179.Google Scholar
[7] Milnor, J., Husemoller, D., Symmetric bilinear forms, Berlin-Heidelberg-New York, Springer 1973.Google Scholar
[8] O’Meara, O. T., Introduction to quadratic forms, Berlin-Heidelberg-New York, Springer 1963.CrossRefGoogle Scholar
[9] Siegel, C. L., Über die analytische Theorie der quadratischen Formen, Ann. of Math., 36 (1935), 527–606.Google Scholar