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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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$GL_{2}(O_K)$-invariant lattices in the space of binary cubic forms with coefficients in the number field $K$
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by Charles A. Osborne PDF
Proc. Amer. Math. Soc. 142 (2014), 2313-2325 Request permission

Abstract:

In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all $GL_{2}(\mathbb {Z})$-invariant lattices in the space of binary cubic forms with coefficients in $\mathbb {Q}$. In this paper, we aim to generalize their result by replacing the rational field with an arbitrary algebraic number field, $K$. We conclude the paper by connecting the lattices described in our main result to a zeta function developed by Datskovsky and Wright, which yields a functional equation for certain Dirichlet series attached to the lattices.
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Additional Information
  • Charles A. Osborne
  • Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
  • Received by editor(s): May 23, 2011
  • Received by editor(s) in revised form: August 2, 2012
  • Published electronically: March 19, 2014
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2313-2325
  • MSC (2010): Primary 11M41, 11R42
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11978-2
  • MathSciNet review: 3195756