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

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

2011-12-06

arxiv.org/abs/1112.1397v2

Mathematics

Number Theory

9 pages (revised; minor corrections from first version)

Scientific paper

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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