English

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.

Keywords

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)