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There are 913 regular ternary forms

Published online by Cambridge University Press:  26 February 2010

William C. Jagy ,
Irving Kaplansky  and
Alexander Schiemann
William C. Jagy
Affiliation:
Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720, U.S.A.
Irving Kaplansky
Affiliation:
Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720, U.S.A.
Alexander Schiemann
Affiliation:
Universitát des Saarlandes, FB9 Mathematik, Postfach 151150, D-66041 Saarbrücken, Germany
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Extract

The forms under discussion are integral positive definite quadratic forms in three variables. Such a form g is called regular if g represents every integer represented by the genus of g. This can be recast in elementary terms: g is regular if the solvability of g≡a (mod n) for every n implies the solvability of g = a.

Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 332 - 341
Copyright
Copyright © University College London 1997

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References

1.Brandt, H. and Intrau, O.. Tabelle reduzierten positiver ternärer quadratischer Formen. Abh. Sächs. Akacl. Wiss. Math.-Nat. Kl., 45 (1958).Google Scholar
2.Dickson, L. E.. Ternary quadratic forms and congruences. Ann. of Math., 28 (1927), 333341.CrossRefGoogle Scholar
3.Hsia, J. S.. Regular positive ternary quadratic forms. Mathematika, 28 (1981), 231238.CrossRefGoogle Scholar
4.Jones, B. W.. Representation by positive ternary quadratic forms. PhD thesis (Univ. of Chicago, 1928).Google Scholar
5.Jones, B. W. and Pall, G.. Regular and semi-regular positive ternary quadratic forms. Ada Mathematics, 70 (1939), 165191.Google Scholar
6.Kaplansky, I.. A second genus of regular ternary forms. Mathematika, 42 (1995), 444447.CrossRefGoogle Scholar
7.Kaplansky, I.. A third genus of regular ternary forms. 1995. Unpublished preprint.CrossRefGoogle Scholar
8.Watson, G. L.. Some problems in the theory of numbers. PhD thesis (Univ. of London, 1953).Google Scholar
9. Watson, G. L.. One-class genera of positive ternary quadratic forms, II. Mathematika, 22 (1975), 111.CrossRefGoogle Scholar
10.Watson, G. L.. Regular positive ternary quadratic forms. J. London Math. Soc., 13 (1976), 97102.CrossRefGoogle Scholar