Nesterenko-like rational function, useful to prove the Apéry’s theorem

Anier Soria Lorente
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 2, Pages 79—91
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Anier Soria Lorente
Department of Basic Sciences
Granma University, Cuba

Abstract

In this paper, a brief introduction to the Apéry’s result and to the so called phenomenon of Apéry’s is given. Here, a modification of the Nesterenko’s rational function, from which new Diophantine approximations to ζ(3) are deduced, is presented. Moreover, as a consequence we deduce the corresponding Apéry-Like recurrence relation as well as a new continued fraction expansion and a new series expansion for ζ(3).

Keywords

  • Riemann zeta function
  • Apéry’s approximants
  • Recurrence relation
  • Continued fraction expansion
  • Irrationality

AMS Classification

  • Primary: 11B37, 30B70, 14G10, 11J72, 11M06
  • Secondary: 37B20, 11A55, 11J70, 11Y55, 11Y65

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Cite this paper

APA

Lorente, A. S. (2014). Nesterenko-like rational function, useful to prove the Apéry’s theorem. Notes on Number Theory and Discrete Mathematics, 20(2), 79-91.

Chicago

Lorente, Anier Soria. “Nesterenko-like Rational Function, Useful to Prove the Apéry’s Theorem.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 79-91.

MLA

Lorente, Anier Soria. “Nesterenko-like Rational Function, Useful to Prove the Apéry’s Theorem.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 79-91. Print.

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