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

Frank Thorne
2014 Proceedings of the American Mathematical Society  
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 [22] in the negative.
doi:10.1090/s0002-9939-2014-12064-8 fatcat:wpsouorbbzg4bdsc44zaavpgvy