Represented value sets for integral binary quadratic forms and lattices

Authors:
A. G. Earnest and Robert W. Fitzgerald

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3765-3770

MSC (2000):
Primary 11E16; Secondary 11E12, 11E25, 11R29

DOI:
https://doi.org/10.1090/S0002-9939-07-08895-8

Published electronically:
August 30, 2007

MathSciNet review:
2341925

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Abstract | References | Similar Articles | Additional Information

Abstract: A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over a Dedekind domain, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property observed by V. Arnold in the case of integral binary quadratic forms.

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Additional Information

**A. G. Earnest**

Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901

Email:
aearnest@math.siu.edu

**Robert W. Fitzgerald**

Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901

Email:
rfitzg@math.siu.edu

DOI:
https://doi.org/10.1090/S0002-9939-07-08895-8

Received by editor(s):
June 14, 2006

Received by editor(s) in revised form:
September 5, 2006

Published electronically:
August 30, 2007

Communicated by:
Ken Ono

Article copyright:
© Copyright 2007
American Mathematical Society

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