Shintani's zeta function is not a finite sum of Euler products
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🧮 math.NT
keywords
eulerfinitefunctionproductsshintanizetaanswersassociated
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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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