Diophantine properties of numbers related to Catalan's constant

Mathematische Annalen

Volumn 326, Issue 4, 2003, Pages 705-721

  Rivoal, T ^a,c   Zudilin, W ^b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c UNIVERSITÉ DE CAEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041917212     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-003-0420-2     Document Type: Article

References (17)

1. [Ap] Apéry, R.: Irrationalité de ζ (2) et ζ (3). Astérisque 61, 11-13 (1979)
2. [Bai] Bailey, W.N.: Generalized hypergeometric series, Cambridge Math. Tracts 32 (Cambridge University Press, Cambridge 1935); 2nd reprinted edition (Stechert-Hafner, New York 1964)
3. [Bak] Baker, A.: The theory of linear forms in logarithms, Transcendence theory: advances and applications (Proc. Conf., Univ. Cambridge, Cambridge, 1976), pp. 1-27 (Academic Press, London (1977))
4. [BR] Ball, K., Rivoal, T.: Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs. Invent. Math. 146(1), 193-207 (2001)
5. [Ha] Hata, M.: Legendre type polynomials and irrationality measures. J. Reine Angew. Math. 407, 99-125 (1990)
6. [Ne] Nesterenko, Yu. V.: On the linear independence of numbers, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 46-54 (1985); English transl., Moscow Univ. Math. Bull. 40, 69-74 (1985)
7. [Ne] Nesterenko, Yu. V.: On the linear independence of numbers, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 46-54 (1985); English transl., Moscow Univ. Math. Bull. 40, 69-74 (1985)
8. [RV] Rhin, G., Viola, C.: On a permutation group related to ζ(2). Acta Arith. 77, 23-56 (1996)
9. [Ri1] Rivoal, T.: La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs. C.R. Acad. Sci. Paris Sér. I Math. 331, 267-270 (2000)
10. [Ri2] Rivoal, T.: Irrationalité d'au moins un des neuf nombres ζ (5), ζ(7),..., ζ(21), Acta Arith. 103, 157-167 (2002)
11. [S1] Slater, L.J.: Generalized hypergeometric functions, 2nd edition (Cambridge University Press, Cambridge 1966)
12. [Zu1] Zudilin, W.: Irrationality of values of Riemann's zêta function, Izv. Ross. Akad. Nauk Ser. Mat. 66, 49-102 (2002); English transl., Russian Acad. Sci. Izv. Math. 66, (2002)
13. [Zu1] Zudilin, W.: Irrationality of values of Riemann's zêta function, Izv. Ross. Akad. Nauk Ser. Mat. 66, 49-102 (2002); English transl., Russian Acad. Sci. Izv. Math. 66, (2002)
14. [Zu2] Zudilin, W.: Arithmetic of linear forms involving odd zeta values, Preprint (August 2001); E-print math.NT/0206176, 42 pages (2002)
15. [Zu3] Zudilin, V.V.: One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational, Uspekhi Mat. Nauk 56(4), 149-150 (2001); English transl., Russian Math. Surveys 56, 774-776 (2001)
16. [Zu3] Zudilin, V.V.: One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational, Uspekhi Mat. Nauk 56(4), 149-150 (2001); English transl., Russian Math. Surveys 56, 774-776 (2001)
17. [Zu4] Zudilin, W.: Apéry-like difference equation for Catalan's constant, E-print math.NT/0201024, 10 pages (2002)