Abstract

We study the zeta functions for the space of binary cubic forms introduced by Shintani. The zeta function is defined for each invariant lattice. We classify the invariant lattices, and investigate explicit relationships between the zeta functions associated with those lattices. We also study the analytic properties of the zeta functions, and rewrite Shintani's functional equation in a self dual form using an explicit relation.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1525-1541
Launched on MUSE
2009-12-05
Open Access
No
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