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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: August 30, 2007
MathSciNet review: 2341925
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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: http://dx.doi.org/10.1090/S0002-9939-07-08895-8
PII: S 0002-9939(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.