V. N. Sorokin, “A transcendence measure for $\pi^2$”, Sb. Math., 187:12 (1996), 1819

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Sbornik: Mathematics, 1996, Volume 187, Issue 12, Pages 1819–1852
DOI: https://doi.org/10.1070/SM1996v187n12ABEH000179 (Mi sm179)

This article is cited in 24 scientific papers (total in 24 papers)

A transcendence measure for

π^{2}

$\pi^2$

V. N. Sorokin

M. V. Lomonosov Moscow State University

English version PDF (929 kB) Citations (24) Russian version article

References:

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DOI: https://doi.org/10.1070/SM1996v187n12ABEH000179

Abstract: A new proof of the fact that

π^{2}

$\pi^2$ is transcendental is proposed. A modification of Hermite's method for an expressly constructed Nikishin system is used. The Beukers integral, which was previously used to prove Apéry's theorem on the irrationality of

ζ (2)

$\zeta (2)$ and

ζ (3)

$\zeta (3)$ is a special case of this construction.

Received: 13.11.1995

Bibliographic databases:

UDC: 517.5

MSC: 11J82, 41A21

Language: English

Original paper language: Russian

Citation: V. N. Sorokin, “A transcendence measure for

π^{2}

$\pi^2$ ”, Sb. Math., 187:12 (1996), 1819–1852

Citation in format AMSBIB

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\by V.~N.~Sorokin

\paper A transcendence measure for $\pi^2$

\jour Sb. Math.

\yr 1996

\vol 187

\issue 12

\pages 1819--1852

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Linking options:

https://www.mathnet.ru/eng/sm179

https://doi.org/10.1070/SM1996v187n12ABEH000179

https://www.mathnet.ru/eng/sm/v187/i12/p87

This publication is cited in the following 24 articles:

Claude Brezinski, Michela Redivo-Zaglia, Extrapolation and Rational Approximation, 2020, 7
Zudilin W., “A Determinantal Approach to Irrationality”, Constr. Approx., 45:2 (2017), 301–310
Fischler S., Rivoal T., “Multiple Zeta Values, Pade Approximation and Vasilyev'S Conjecture”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 15:SI (2016), 1–24
Stéphane Fischler, “Nesterenko's linear independence criterion for vectors”, Monatsh Math, 177:3 (2015), 397
W. Zudilin, “Arithmetic hypergeometric series”, Russian Math. Surveys, 66:2 (2011), 369–420
Cresson, PJ, “Multiple hypergeometric series and polyzetas”, Bulletin de La Societe Mathematique de France, 136:1 (2008), 97
C. Krattenthaler, T. Rivoal, “An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series”, Ramanujan J, 13:1-3 (2007), 203
Salah Boukraa, Saoud Hassani, Jean-Marie Maillard, Nadjah Zenine, “From Holonomy of the Ising Model Form Factors to $n$ -Fold Integrals and the Theory of Elliptic Curves”, SIGMA, 3 (2007), 099, 43 pp.
Boukraa, S, “Singularities of n-fold integrals of the Ising class and the theory of elliptic curves”, Journal of Physics A-Mathematical and Theoretical, 40:39 (2007), 11713
Georges Rhin, Carlo Viola, “Multiple integrals and linear forms in zeta-values”, Funct. Approx. Comment. Math., 37:2 (2007)
Yu. V. Nesterenko, “On an Identity of Mahler”, Math. Notes, 79:1 (2006), 97–108
Huttner, M, “Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions”, Israel Journal of Mathematics, 153 (2006), 1
S. A. Zlobin, “Expansion of Multiple Integrals in Linear Forms”, Math. Notes, 77:5 (2005), 630–652
Fischler, S, “Irrationality of zeta values”, Asterisque, 2004, no. 294, 27
Zlobin, SA, “Decompositions of multiple integrals into linear forms”, Doklady Mathematics, 70:2 (2004), 758
E. A. Ulanskii, “Identities for Generalized Polylogarithms”, Math. Notes, 73:4 (2003), 571–581
S. A. Zlobin, “Integrals Expressible as Linear Forms in Generalized Polylogarithms”, Math. Notes, 71:5 (2002), 711–716
V. N. Sorokin, “Cyclic graphs and Apéry's theorem”, Russian Math. Surveys, 57:3 (2002), 535–571
W. V. Zudilin, “Very well-poised hypergeometric series and multiple integrals”, Russian Math. Surveys, 57:4 (2002), 824–826
Fischler, S, “Linear forms in multiple zeta values and multiple integrals”, Comptes Rendus Mathematique, 335:1 (2002), 1

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

Statistics & downloads:
Abstract page:	671
Russian version PDF:	355
English version PDF:	40
References:	69
First page:	2

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