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Mat. Zametki, 2006, Volume 79, Issue 4, Pages 607–618 (Mi mz2731)  

This article is cited in 2 scientific papers (total in 2 papers)

Irrationality of the sums of zeta values

T. G. Hessami Pilehrood, Kh. Hessami Pilehrood

Shahrekord University

Abstract: In this paper, we establish a lower bound for the dimension of the vector spaces spanned over $\mathbb Q$ by 1 and the sums of the values of the Riemann zeta function at even and odd points. As a consequence, we obtain numerical results on the irrationality and linear independence of the sums of zeta values at even and odd points from a given interval of the positive integers.

DOI: https://doi.org/10.4213/mzm2731

Full text: PDF file (234 kB)
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English version:
Mathematical Notes, 2006, 79:4, 561–571

Bibliographic databases:

UDC: 511.3
Received: 13.04.2005

Citation: T. G. Hessami Pilehrood, Kh. Hessami Pilehrood, “Irrationality of the sums of zeta values”, Mat. Zametki, 79:4 (2006), 607–618; Math. Notes, 79:4 (2006), 561–571

Citation in format AMSBIB
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\issue 4
\pages 607--618
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  • https://doi.org/10.4213/mzm2731
  • http://mi.mathnet.ru/eng/mz/v79/i4/p607

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fischler S., “Distribution of Irrational Zeta Values”, Bull. Soc. Math. Fr., 145:3 (2017), 381–409  crossref  mathscinet  zmath  isi  scopus
    2. Krattenthaler Ch., Zudilin W., “Hypergeometry Inspired By Irrationality Questions”, Kyushu J. Math., 73:1 (2019), 189–203  crossref  isi
  • Математические заметки Mathematical Notes
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