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

Published 6 Dec 2011 in math.NT | (1112.1397v3)

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

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