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Computing the moment polynomials of the zeta function


Authors: Michael O. Rubinstein and Shuntaro Yamagishi
Journal: Math. Comp. 84 (2015), 425-454
MSC (2010): Primary 11M06, 11M50; Secondary 15B52
DOI: https://doi.org/10.1090/S0025-5718-2014-02845-7
Published electronically: June 4, 2014
MathSciNet review: 3266969
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Abstract: We describe a method to accelerate the numerical computation of the coefficients of the polynomials $ P_k(x)$ that appear in the conjectured asymptotics of the $ 2k$-th moment of the Riemann zeta function. We carried out our method to compute the moment polynomials for $ k \leq 13$, and used these to experimentally test conjectures for the moments up to height $ 10^8$.


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Additional Information

Michael O. Rubinstein
Affiliation: University of Waterloo, Department of Pure Mathematics, 200 University Avenue W, Waterloo, ON N2L 3G1 Canada.
Email: michael.o.rubinstein@gmail.com

Shuntaro Yamagishi
Affiliation: University of Waterloo, Department of Pure Mathematics, 200 University Avenue W, Waterloo, ON N2L 3G1 Canada.
Email: syamagishi@uwaterloo.ca

DOI: https://doi.org/10.1090/S0025-5718-2014-02845-7
Received by editor(s): March 1, 2012
Received by editor(s) in revised form: May 14, 2013
Published electronically: June 4, 2014
Additional Notes: This work was supported by the National Science Foundation under awards DMS-0757627 (FRG grant), and an NSERC Discovery Grant.
Article copyright: © Copyright 2014 American Mathematical Society