GL 2 (O K )-INVARIANT LATTICES IN THE SPACE OF BINARY CUBIC FORMS WITH COEFFICIENTS IN THE NUMBER FIELD K

GL 2 (O K )-INVARIANT LATTICES IN THE SPACE OF BINARY CUBIC FORMS WITH COEFFICIENTS IN THE NUMBER FIELD K

In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all GL 2 (ℤ)-invariant lattices in the space of binary cubic forms with coefficients in 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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society Vol. 142; no. 7; pp. 2313 - 2325
Main Author: OSBORNE, CHARLES A.
Format: Journal Article
Language:English
Published: AMERICAN MATHEMATICAL SOCIETY 01-07-2014
Subjects:
Algebra
Coefficients
Coordinate systems
Cubic functions
Discriminants
Integers
Mathematical functions
Mathematical lattices
Mathematical rings
Numbers
Online Access:Get full text
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Summary:In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all GL 2 (ℤ)-invariant lattices in the space of binary cubic forms with coefficients in 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.
ISSN:0002-9939
1088-6826