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A note on finite Euler product approximations of the Riemann zeta-function


Author: Steven M. Gonek
Journal: Proc. Amer. Math. Soc. 143 (2015), 3295-3302
MSC (2010): Primary 11M06, 11M26
Published electronically: April 6, 2015
MathSciNet review: 3348772
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Abstract: We construct a family of approximations of the Riemann zeta-function and a closely related function formed from finite Euler products, the pole of the zeta-function, and any zeros the zeta-function might have in the right half of the critical strip. The analysis is unconditional and suggests that if the Riemann Hypothesis is false, then the zeta-function's zeros ``arise'' in two ways.


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Additional Information

Steven M. Gonek
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: gonek@math.rochester.edu

DOI: https://doi.org/10.1090/proc/12380
Keywords: Riemann zeta-function, Euler products, zeros of the zeta-function
Received by editor(s): April 20, 2013
Received by editor(s) in revised form: October 7, 2013
Published electronically: April 6, 2015
Additional Notes: Research of the author was supported in part by NSF grant DMS-1200582.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.