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Positive ternary quadratic forms with finitely many exceptions

Authors: Wai Kiu Chan and Byeong-Kweon Oh
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1567-1573
MSC (2000): Primary 11E12, 11E20
Published electronically: January 27, 2004
MathSciNet review: 2051115
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Abstract | References | Similar Articles | Additional Information

Abstract: An integral quadratic form $f$ is said to be almost regular if $f$ globally represents all but finitely many integers that are represented by the genus of $f$. In this paper, we study and characterize all almost regular positive definite ternary quadratic forms.

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  • 1. W. K. Chan and A. G. Earnest, Discriminant bounds for spinor regular ternary quadratic lattices, submitted.
  • 2. W. K. Chan and B.-K. Oh, Finiteness theorems for positive definite $n$-regular quadratic forms, Trans. Amer. Math. Soc., 355 (2003), 2385-2396.
  • 3. W. Duke and R. Schulze-Pillot, Representations of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids, Invent. Math., 99 (1990), 49-57. MR 90m:11051
  • 4. A. G. Earnest, Representations of spinor exceptional integers by ternary quadratic forms, Nagoya Math. J., 93 (1984), 27-38. MR 85j:11042
  • 5. A. G. Earnest, J. S. Hsia and D. C. Hung, Primitive representations by spinor genera of ternary quadratic forms, J. London Math. Soc. (2), 50 (1994), 222-230. MR 95k:11044
  • 6. J. S. Hsia and M. Jöchner, Almost strong approximations for definite quadratic spaces, Invent. Math., 129 (1997), 471-487. MR 98m:11025
  • 7. J. S. Hsia, Y. Kitaoka and M. Kneser, Representations of positive definite quadratic forms, J. Reine Angew. Math., 301 (1978), 132-141. MR 58:27758
  • 8. W. C. Jagy, I. Kaplansky and A. Schiemann, There are $913$ regular ternary forms, Mathematika, 44 (1997), 332-341. MR 99a:11046
  • 9. Y. Kitaoka, Arithmetic of quadratic forms, Cambridge University Press, 1993. MR 95c:11044
  • 10. O. T. O'Meara, Introduction to quadratic forms, Springer-Verlag, New York, 1963. MR 27:2485
  • 11. R. Schulze-Pillot, Exceptional integers for genera of integral ternary positive definite quadratic forms, Duke Math. J., 102, No. 2 (2000), 351-357. MR 2001a:11068
  • 12. W. Tartakowsky, Die Gesamtheit der Zahlen, die durch eine positive quadratische Form $F(x_1, \ldots, x_s)$ $(s \geq 4)$ darstellbar sind, Izv. Akad. Nauk SSSR, 7 (1929), 111-122, 165-195.
  • 13. G. L. Watson, Some problems in the theory of numbers, Ph.D. Thesis, University of London, 1953.
  • 14. G. L. Watson, The representation of integers by positive ternary quadratic forms, Mathematika 1 (1954), 104-110. MR 16:680c
  • 15. G. L. Watson, The class-number of a positive quadratic form, Proc. London Math. Soc. 13 (1963), 549-576. MR 27:107
  • 16. G. L. Watson, One-class genera of positive ternary quadratic forms, Mathematika, 19 (1972), 96-104. MR 47:3317
  • 17. G. L. Watson, Regular positive ternary quadratic forms, J. London Math. Soc. (2) 13 (1976), 97-102. MR 54:2590

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Additional Information

Wai Kiu Chan
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459

Byeong-Kweon Oh
Affiliation: Department of Applied Mathematics, Sejong University, Seoul 143-747, Korea

Received by editor(s): October 15, 2002
Published electronically: January 27, 2004
Additional Notes: The research of the first author is partially supported by the National Security Agency and the National Science Foundation
The work of the second author was supported by KOSEF Grant # 98-0701-01-05-L
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2004 American Mathematical Society

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