Shintani's zeta function is not a finite sum of Euler products

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.

10 pages (lightly further revised; to appear in Proc. AMS)

References in corpus (3)

• Counting Cubic Extensions with given Quadratic Resolvent
• Orbital L-functions for the space of binary cubic forms
• On the Davenport-Heilbronn theorems and second order terms