On a permutation group related to ζ(2)

Georges Rhin; Carlo Viola

Acta Arithmetica (1996)

  • Volume: 77, Issue: 1, page 23-56
  • ISSN: 0065-1036

How to cite


Georges Rhin, and Carlo Viola. "On a permutation group related to ζ(2)." Acta Arithmetica 77.1 (1996): 23-56. <http://eudml.org/doc/206906>.

author = {Georges Rhin, Carlo Viola},
journal = {Acta Arithmetica},
keywords = {permutation group; ; -adic valuations; JFM 35.0320.01; Riemann zeta-function; irrationality measure},
language = {eng},
number = {1},
pages = {23-56},
title = {On a permutation group related to ζ(2)},
url = {http://eudml.org/doc/206906},
volume = {77},
year = {1996},

AU - Georges Rhin
AU - Carlo Viola
TI - On a permutation group related to ζ(2)
JO - Acta Arithmetica
PY - 1996
VL - 77
IS - 1
SP - 23
EP - 56
LA - eng
KW - permutation group; ; -adic valuations; JFM 35.0320.01; Riemann zeta-function; irrationality measure
UR - http://eudml.org/doc/206906
ER -


  1. [1] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268-272. Zbl0421.10023
  2. [2] A. C. Dixon, On a certain double integral, Proc. London Math. Soc. (2) 2 (1905), 8-15. Zbl35.0320.01
  3. [3] R. Dvornicich and C. Viola, Some remarks on Beukers' integrals, in: Colloq. Math. Soc. János Bolyai 51, Budapest, 1987, 637-657. Zbl0755.11019
  4. [4] A. Erdélyi et al., Higher Transcendental Functions (Bateman Manuscript Project), Vol. 1, McGraw-Hill, New York, 1953. Zbl0051.30303
  5. [5] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125. Zbl0692.10034
  6. [6] M. Hata, Rational approximations to π and some other numbers, Acta Arith. 63 (1993), 335-349. 
  7. [7] M. Hata, A note on Beukers' integral, J. Austral. Math. Soc. A 58 (1995), 143-153. Zbl0830.11026
  8. [8] G. Rhin and C. Viola, On the irrationality measure of ζ(2), Ann. Inst. Fourier (Grenoble) 43 (1993), 85-109. 
  9. [9] E. A. Rukhadze, A lower bound for the approximation of ln 2 by rational numbers, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1987 (6), 25-29 (in Russian). Zbl0635.10025

Citations in EuDML Documents

  1. Georges Rhin, Carlo Viola, The permutation group method for the dilogarithm
  2. Francesco Amoroso, Carlo Viola, Approximation measures for logarithms of algebraic numbers
  3. Carlo Viola, Approssimazione diofantea, frazioni continue e misure d’irrazionalità
  4. Ville Merilä, q-Hypergeometric Functions and Irrationality Measures
  5. Carlo Viola, Birational transformations and values of the Riemann zeta-function
  6. Stéphane Fischler, Groupes de Rhin-Viola et intégrales multiples
  7. Tanguy Rivoal, Séries hypergéométriques et irrationalité des valeurs de la fonction zêta de Riemann
  8. Wadim Zudilin, Well-poised hypergeometric service for diophantine problems of zeta values
  9. Wadim Zudilin, Arithmetic of linear forms involving odd zeta values
  10. Carlo Viola, Gruppi di permutazioni e risultati di irrazionalità

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