-invariant lattices in the space of binary cubic forms with coefficients in the number field

Author:
Charles A. Osborne

Journal:
Proc. Amer. Math. Soc. **142** (2014), 2313-2325

MSC (2010):
Primary 11M41, 11R42

Published electronically:
March 19, 2014

MathSciNet review:
3195756

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Abstract | References | Similar Articles | Additional Information

Abstract: In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all -invariant lattices in the space of binary cubic forms with coefficients in . In this paper, we aim to generalize their result by replacing the rational field with an arbitrary algebraic number field, . 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

DOI:
http://dx.doi.org/10.1090/S0002-9939-2014-11978-2

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

Article copyright:
© Copyright 2014
American Mathematical Society

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