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

DOI:
https://doi.org/10.1090/S0002-9939-04-07433-7

Published electronically:
January 27, 2004

MathSciNet review:
2051115

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

**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**-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**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**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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
11E12,
11E20

Retrieve articles in all journals with MSC (2000): 11E12, 11E20

Additional Information

**Wai Kiu Chan**

Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459

Email:
wkchan@wesleyan.edu

**Byeong-Kweon Oh**

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

Email:
bkoh@sejong.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-04-07433-7

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