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

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dc.creatorOhno, Yasuo
dc.creatorTaniguchi, Takashi
dc.creatorWakatsuki, Satoshi
dc.date2007-11-04
dc.date.accessioned2026-07-07T08:40:35Z
dc.date.available2026-07-07T08:40:35Z
dc.descriptionWe study the class numbers of integral binary cubic forms. For each $SL_2(Z)$ 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.
dc.description14pages
dc.identifierhttps://arxiv.org/abs/0711.0499
dc.identifierhttp://arxiv.org/abs/0711.0499
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141413
dc.subjectNumber Theory
dc.subject11M41
dc.titleOn relations among Dirichlet series whose coefficients are class numbers of binary cubic forms
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