Orbital L-functions for the space of binary cubic forms
Number Theory
2019-06-12 v1
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).
Cite
@article{arxiv.1112.5030,
title = {Orbital L-functions for the space of binary cubic forms},
author = {Takashi Taniguchi and Frank Thorne},
journal= {arXiv preprint arXiv:1112.5030},
year = {2019}
}
Comments
49 pages; submitted