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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Represented value sets for integral binary quadratic forms and lattices
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by A. G. Earnest and Robert W. Fitzgerald PDF
Proc. Amer. Math. Soc. 135 (2007), 3765-3770 Request permission

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.
References
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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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2341925