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Limit theorems for the coefficients of the modified Borwein method for the calculation of the Riemann zeta-function values

Volume 151 / 2018

Igoris Belovas, Leonidas Sakalauskas Colloquium Mathematicum 151 (2018), 217-227 MSC: 05A16, 11M99, 60F05. DOI: 10.4064/cm7086-2-2017 Published online: 18 December 2017

Abstract

Numerical experiments as well as practical applications of zeta-functions require a great amount of computations. We introduce a modification of one of the efficient methods for calculating the Riemann zeta-function values—Borwein’s algorithm. We prove local and central limit theorems for the coefficients of a modified version of the method, as well as establish convergence rates to the limiting law. An asymptotic expression is derived for the coefficients of the modified version of the method. Calculation of the zeta-values with the resulting approximation is discussed.

Authors

  • Igoris BelovasVilnius University Institute
    of Mathematics and Informatics
    LT-08663 Vilnius, Lithuania
    e-mail
  • Leonidas SakalauskasVilnius University Institute
    of Mathematics and Informatics
    LT-08663 Vilnius, Lithuania
    and
    Vilnius Gediminas Technical University
    LT-10223 Vilnius, Lithuania

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