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

Thorne, Frank

doi:10.1090/S0002-9939-2014-12064-8

Shintani’s zeta function is not a finite sum of Euler products
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Proc. Amer. Math. Soc. 142 (2014), 1943-1952 Request permission

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.

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