Orbital L-functions for the space of binary cubic forms

Details Orbital L-functions for the space of binary cubic forms Orbital L-functions for the space of binary cubic forms

2011-12-21

arxiv.org/abs/1112.5030v1

Mathematics

Number Theory

49 pages; submitted

Scientific paper

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).

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