On relations among Dirichlet series whose coefficients are class numbers of binary cubic forms

@inproceedings{Ohno2007OnRA,
  title={On relations among Dirichlet series whose coefficients are class numbers of binary cubic forms},
  author={Ohno and Taniguchi and Wakatsuki},
  year={2007}
}
We study the class numbers of integral binary cubic forms. For each SL2(Z) invariant lattice L, Shintani introduced Dirichlet series whose coefficients are the class numbers of binary cubic forms in L. We classify the invariant lattices, and investigate explicit relationships between Dirichlet series associated with those lattices. We also study the analytic properties of the Dirichlet series, and rewrite the functional equation in a self dual form using the explicit relationship. 

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