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Diophantine properties of numbers related to Catalan's constant

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posted on 2025-05-09, 05:18 authored by T. Rivoal, W. Zudilin
This article deals with Dirichlet’s beta function. Using the recursion (37), we have verified numerically (up to n = 1000) that 16ⁿ ·un ∊ℤand d²₂n · 16ⁿ · vn ∊ℤ: this is more that one can get from Lemma 6, although it is not sufficient to prove the irrationality of Catalan’s constant.

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Related Materials

  1. 1.
    DOI - Is published in https://doi.org/10.1007/s00208-003-0420-2
  2. 2.
    ISSN - Is version of https://portal.issn.org/resource/ISSN/0025-5831

Journal title

Mathematische Annalen

Volume

326

Issue

4

Pagination

705-721

Publisher

Springer-Verlag

Language

  • en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Mathematical and Physical Sciences

Rights statement

The final publication is available at www.springerlink.com

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    Keywords

    Catalan's constantDirichlet’s beta functionintegersLindemann’s theorem

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