Finiteness theorems for positive definite -regular quadratic forms

Authors:
Wai Kiu Chan and Byeong-Kweon Oh

Journal:
Trans. Amer. Math. Soc. **355** (2003), 2385-2396

MSC (2000):
Primary 11E12, 11E20

Published electronically:
January 27, 2003

MathSciNet review:
1973994

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Abstract: An integral quadratic form of variables is said to be -regular if globally represents all quadratic forms of variables that are represented by the genus of . For any , it is shown that up to equivalence, there are only finitely many primitive positive definite integral quadratic forms of variables that are -regular. We also investigate similar finiteness results for almost -regular and spinor -regular quadratic forms. It is shown that for any , there are only finitely many equivalence classes of primitive positive definite spinor or almost -regular quadratic forms of variables. These generalize the finiteness result for 2-regular quaternary quadratic forms proved by Earnest (1994).

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Additional Information

**Wai Kiu Chan**

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

Email:
wkchan@wesleyan.edu

**Byeong-Kweon Oh**

Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Address at time of publication:
School of Computational Sciences, Korea Institute for Advanced Study, 207-43 Cheongyangri-dong, Dongdaemun-gu Seoul 130-012, Korea

Email:
bkoh@newton.kias.re.kr

DOI:
http://dx.doi.org/10.1090/S0002-9947-03-03262-8

Keywords:
Regular integral quadratic forms

Received by editor(s):
July 13, 2002

Received by editor(s) in revised form:
November 19, 2002

Published electronically:
January 27, 2003

Additional Notes:
The research of the first author is partially supported by the National Security Agency and the National Science Foundation

The second author was supported by a postdoctoral fellowship program from the Korea Science and Engineering Foundation (KOSEF)

Article copyright:
© Copyright 2003
American Mathematical Society