Finiteness theorems for positive definite regular quadratic forms
Authors:
Wai Kiu Chan and ByeongKweon Oh
Journal:
Trans. Amer. Math. Soc. 355 (2003), 23852396
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 2regular 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
ByeongKweon 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, 20743 Cheongyangridong, Dongdaemungu Seoul 130012, Korea
Email:
bkoh@newton.kias.re.kr
DOI:
http://dx.doi.org/10.1090/S0002994703032628
PII:
S 00029947(03)032628
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
