𝐺𝐿₂(𝑂_{𝐾})-invariant lattices in the space of binary cubic forms with coefficients in the number field 𝐾

Osborne, Charles

doi:10.1090/S0002-9939-2014-11978-2

$GL_{2}(O_K)$-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.

References

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