On a permutation group related to ζ(2)

 Access to full text

 Full (PDF)

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

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