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A central limit theorem for coefficients of the modified Borwein method for the calculation of the Riemann zeta-function

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Abstract

The paper extends the study of the modified Borwein method for the calculation of the Riemann zeta-function. We present an alternative perspective on the proof of the central limit theorem for coefficients of the method. The new approach is based on the connection with the limit theorem applied to asymptotic enumeration.

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References

  1. I. Belovas and L. Sakalauskas, Limit theorems for the coefficients of the modified Borwein method for the calculation of the Riemann zeta-function values, Colloq. Math., 151(2):217–227, 2018, available from: https://doi.org/10.4064/cm7086-2-2017.

  2. E.A. Bender, Central and local limit theorems applied to asymptotic enumeration, J. Comb. Theory, Ser. A, 15:91–111,1973.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Borwein, An efficient algorithm for the Riemann zeta function, in M. Théra (Ed.), Constructive, Experimental, and Nonlinear Analysis, CMS Conf. Proc., Vol. 27, AMS, Providence, RI, 2000, pp. 29–34.

  4. H.-K. Hwang, On convergence rates in the central limit theorems for combinatorial structures, Eur. J. Comb., 19(3): 329–343, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.M. Odlyzko, Asymptotic enumeration methods, in R.L. Graham, M. Groetschel, and L. Lovasz (Eds.), Handbook of Combinatorics, Vol. 2, Elsevier, Amsterdam, 1995, pp. 1063–1229.

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Correspondence to Igoris Belovas.

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Dedicated to Professors Antanas Laurinčikas and Eugenijus Manstavičius on the occasion of their 70th birthdays

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Belovas, I. A central limit theorem for coefficients of the modified Borwein method for the calculation of the Riemann zeta-function. Lith Math J 59, 17–23 (2019). https://doi.org/10.1007/s10986-019-09421-4

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  • DOI: https://doi.org/10.1007/s10986-019-09421-4

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