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


Author: Frank Thorne
Journal: Proc. Amer. Math. Soc. 142 (2014), 1943-1952
MSC (2010): Primary 11M41, 11R16
DOI: https://doi.org/10.1090/S0002-9939-2014-12064-8
Published electronically: March 5, 2014
MathSciNet review: 3182013
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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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Additional Information

Frank Thorne
Affiliation: Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, South Carolina 29201
Email: thorne@math.sc.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12064-8
Received by editor(s): July 11, 2012
Published electronically: March 5, 2014
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.