Glasnik Matematicki, Vol. 54, No. 1 (2019), 1-9.

A LOCAL LIMIT THEOREM FOR COEFFICIENTS OF MODIFIED BORWEIN'S METHOD

Igoris Belovas

Vilnius University, Institute of Data Science and Digital Technologies, Akademijos st. 4, 08412 Vilnius, Lithuania
and
Vilnius Gediminas Technical University , 10223 Vilnius, Lithuania
e-mail: Igoris.Belovas@mii.vu.lt

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

2010 Mathematics Subject Classification.   05A16, 11M99

Key words and phrases.   Local limit theorem, asymptotic enumeration, asymptotic normality

https://doi.org/10.3336/gm.54.1.01

References:

1. I. Belovas, L. Sakalauskas, Limit theorems for the coefficients of the modified Borwein method for the calculation of the Riemann zeta-function values, Colloq. Math. 151 (2018), 217-227.
   MathSciNet     CrossRef

2. I. Belovas, A central limit theorem for coefficients of the modified Borwein method for the calculation of the Riemann zeta-function, Lith. Math. J. 59 (2019), 17-23.
   MathSciNet     CrossRef

3. E. A. Bender, Central and local limit theorems applied to asymptotic enumeration, J. Combin. Theory Ser. A. 15 (1973), 91-111.
   MathSciNet     CrossRef

4. P. Borwein, An efficient algorithm for the Riemann Zeta function, in: Constructive, Experimental, and Nonlinear Analysis (Limoges, 1999), CRC, Boca Raton, 2000, 29-34.
   MathSciNet    

5. H.-K. Hwang, On convergence rates in the central limit theorems for combinatorial structures European J. Combin., 19 (1998), 329-343.
   MathSciNet     CrossRef

6. A. M. Odlyzko, Asymptotic enumeration methods, in: Handbook of Combinatorics, vol. 2, Elsevier Sci. B. V., Amsterdam, 1995, 1063-1229.
   MathSciNet