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

Frank Thorne

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arXiv · 1112.1397

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

Frank Thorne

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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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Frank Thorne. 2012-11-09. Shintani's zeta function is not a finite sum of Euler products. https://arxiv.org/abs/1112.1397

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