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Regular positive ternary quadratic forms

Published online by Cambridge University Press:  26 February 2010

J. S. Hsia
J. S. Hsia
Affiliation:
Department of Mathematics, Ohio State University. 231 W. 18th Avenue, Columbus. Ohio 43210, U.S.A.
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Extract

Unless stated otherwise all quadratic forms have rational integer coefficients and all representations are integral representations. For positive binary quadratic forms of the same discriminant it is known that two such forms are equivalent provided they represent the same integers. See, for instance, [Ki2], and for a sharper extension [W2]. On the other hand, in the quaternary case these value-sets are far from characterizing the forms even within a genus. It is therefore natural to ask for positive ternary forms the corresponding question, whose answer appears to be unknown.

Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 231 - 238
Copyright
Copyright © University College London 1981

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References

BH.Benham, J. W. and Hsia, J. S.. “On spinor exceptional representations”, Nayoya Math. J., to appear in Vol. 87 (1982).Google Scholar
BI.Brandt, H. and Intrau, O.. Tabellen reduzierter positiver ternärer quadratischer Formen (Akademie-Verlag, Berlin, 1959).Google Scholar
D.Dickson, L. E.. “Ternary quadratic forms and congruences”, Ann. Math., 28 (1927), 333–341.CrossRefGoogle Scholar
EH.Earnest, A. G. and Hsia, J. S.. “Spinor norms of local integral rotations II”, Pacific J. Math., 61 (1975), 71–86.CrossRefGoogle Scholar
HKK.Hsia, J. S., Kitaoka, Y. and Kneser, M.. “Representations of positive definite quadratic forms”, J. reine angew. Math., 301 (1978), 132–141.Google Scholar
JP.Jones, B. W. and Pall, G.. “Regular and semi-regular positive ternary quadratic forms”, Acta. Math., 70 (1940), 165–191.CrossRefGoogle Scholar
Ki1.Kitaoka, Y.. “On the relation between the positive definite quadratic forms with the same representation numbers”, Proc. Japan Acad., 47 (1971), 439–441.Google Scholar
Ki2.Kitaoka, Y.. “Representations of quadratic forms and their application to Selberg's zeta functions”, Nagoya Math. J., 63 (1976), 153–162.CrossRefGoogle Scholar
K1.Kneser, M.. “Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen”, Arch. Math., 7 (1956), 323–332.CrossRefGoogle Scholar
K2.Kneser, M.. Quadratische Formen (Vorlesungsausarbeitung, Göttingen, 1973/4).Google Scholar
OM.O'Meara, O. T.. Introduction to Quadratic Forms (Springer-Verlag, Berlin, 1963).CrossRefGoogle Scholar
SP1.Schulze-Pillot, R.. “Darstellung durch Spiriorgeschlechte ternäre quadratische Formen”, J. Number Theory, 12 (1980), 529–540.CrossRefGoogle Scholar
SP2.Schulze-Pillot, R.. “Darstellung durch definitive ternare quadratische Formen”, J. Number Theory, to appear.Google Scholar
W1.Watson, G. L.. “Regular positive ternary quadratic forms”. J. London Math. Soc., 13 (1976), 97–102.CrossRefGoogle Scholar
W2.Watson, G. L.. “Determination of a binary quadratic form by its values at integer points”, Mathematika, 26 (1979), 72–75, and 27 (1980), 188.CrossRefGoogle Scholar