Orbital L-functions for the space of binary cubic forms

Abstract

We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from the intrinsic interest, results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper (arXiv:1102.2914).

49 pages; submitted

References in corpus (1)

• Secondary terms in counting functions for cubic fields

Cited by in corpus (9)

• Secondary terms in counting functions for cubic fields
• The shape of cubic fields
• Orbital exponential sums for prehomogeneous vector spaces
• The local zeta function in enumerating quartic fields
• The shape of quartic fields
• On generalization of a theorem of Harish-Chandra
• Eisenstein series twisted Shintani zeta function
• An error estimate for counting $S_3$-sextic number fields
• Shintani's zeta function is not a finite sum of Euler products