Definite regular quadratic forms over

Authors:
Wai Kiu Chan and Joshua Daniels

Journal:
Proc. Amer. Math. Soc. **133** (2005), 3121-3131

MSC (2000):
Primary 11E12, 11E20

DOI:
https://doi.org/10.1090/S0002-9939-05-08197-9

Published electronically:
June 20, 2005

MathSciNet review:
2160173

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a power of an odd prime, and be the ring of polynomials over a finite field of elements. A quadratic form over is said to be regular if globally represents all polynomials that are represented by the genus of . In this paper, we study definite regular quadratic forms over . It is shown that for a fixed , there are only finitely many equivalence classes of regular definite primitive quadratic forms over , regardless of the number of variables. Characterizations of those which are universal are also given.

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Additional Information

**Wai Kiu Chan**

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

Email:
wkchan@wesleyan.edu

**Joshua Daniels**

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

Address at time of publication:
2920 Deakin Street #1, Berkeley, California 94705

Email:
jdaniels@wesleyan.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08197-9

Received by editor(s):
May 21, 2004

Published electronically:
June 20, 2005

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

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.