Shintani's zeta function is not a finite sum of Euler products
Number Theory
2012-11-13 v3
Abstract
We prove that the Shintani zeta function associated to the space of binary cubic forms cannot be written as a finite sum of Euler products. Our proof also extends to several closely related Dirichlet series. This answers a question of Wright in the negative.
Cite
@article{arxiv.1112.1397,
title = {Shintani's zeta function is not a finite sum of Euler products},
author = {Frank Thorne},
journal= {arXiv preprint arXiv:1112.1397},
year = {2012}
}
Comments
10 pages (lightly further revised; to appear in Proc. AMS)