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Matematicheskie Zametki, 2006, Volume 79, Issue 4, Pages 607–618
DOI: https://doi.org/10.4213/mzm2731 (Mi mzm2731) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Irrationality of the sums of zeta values

T. G. Hessami Pilehrood, Kh. Hessami Pilehrood

Shahrekord University
Full-text PDF (234 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm2731
Abstract: In this paper, we establish a lower bound for the dimension of the vector spaces spanned over 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.
Received: 13.04.2005
English version:
Mathematical Notes, 2006, Volume 79, Issue 4, Pages 561–571
DOI: https://doi.org/10.1007/s11006-006-0063-1
Bibliographic databases:
UDC: 511.3
Language: Russian
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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  • https://doi.org/10.4213/mzm2731
  • https://www.mathnet.ru/eng/mzm/v79/i4/p607
    • This publication is cited in the following 4 articles:
    1. Fischler S., “Irrationality of Values of l-Functions of Dirichlet Characters”, J. Lond. Math. Soc.-Second Ser., 101:2 (2020), 857–876  crossref  mathscinet  isi
    2. Krattenthaler Ch., Zudilin W., “Hypergeometry Inspired By Irrationality Questions”, Kyushu J. Math., 73:1 (2019), 189–203  crossref  mathscinet  isi
    3. Fischler S., “Distribution of Irrational Zeta Values”, Bull. Soc. Math. Fr., 145:3 (2017), 381–409  crossref  mathscinet  zmath  isi  scopus
    4. Matilde N. Lalín, Mathew D. Rogers, “Variations of the Ramanujan polynomials and remarks on ζ(2j+1)/π2j+1”, Funct. Approx. Comment. Math., 48:1 (2013)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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