Well-poised hypergeometric transformations of Euler-type multiple integrals

Journal of the London Mathematical Society

Volumn 70, Issue 1, 2004, Pages 215-230

  Zudilin, W ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344700220     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610704005472     Document Type: Article

References (28)

1. G.E. ANDREWS, 'The well-poised thread: an organized chronicle of some amazing summations and their implications', Ramanujan J. 1 (1997) 7-23.
2. R. APÉRY, 'Irrationalité de ζ(2) et ζ(3)', Astérisque 61 (Société Mathématique de France, Paris, 1979) 11-13.
3. W. N. BAILEY, 'Some identities involving generalized hypergeometric series', Proc. London Math. Soc. (2) 29 (1929) 503-516.
4. W. N. BAILEY, 'Some transformations of generalized hypergeometric series and contour integrals of Barnes's type', Quart. J. Math. Oxford 3 (1932) 168-182.
5. W. N. BAILEY, Generalized hypergeometric series, Cambridge Mathematical Tracts 32 (Cambridge University Press, 1935), 2nd reprinted edn (Stechert-Hafner, New York, 1964).
6. E. W. BARNES, 'A new development of the theory of the hypergeometric functions', Proc. London Math. Soc. (2) 6 (1908) 141-177.
7. F. BEUKERS, 'A note on the irrationality of ζ(2) and ζ(3)', Bull. London Math. Soc. 11 (1979) 268-272.
8. H. COHEN, 'Accélération de la convergence de certaines récurrences linéaires', Séminaire de Théorie des Nombres de Bordeaux (1980-81).
9. S. FISCHLER, 'Irrationalité de valeurs de zêta [d'après Apéry, Rivoal, ...]', Séminaire Bourbaki 2002-2003, Exposé 910 (2002) (e-print math.NT/0303066).
10. L. A. GUTNIK, 'On the irrationality of some quantities containing ζ(3)', Amer. Math. Soc. Transl. Ser. 2 140 (1988) 45-55.
11. Yu. L. LUKE, Mathematical functions and their approximations (Academic Press, New York, 1975).
12. Yu. V. NESTERENKO, 'A few remarks on ζ(3)', Mat. Zametki 59 (1996) 865-880.
13. Yu. V. NESTERENKO, 'Integral identities and constructions of approximations to zeta values', J. Théor. Nombres Bordeaux 15 (2003) 535-550 (Actes des 12èmes Rencontres Arithmétiques de Caen (29-30 June 2001)).
14. G. RHIN and C. VIOLA, 'On a permutation group related to ζ(2)', Acta Arith. 77 (1996) 23-56.
15. G. RHIN and C. VIOLA, 'The group structure for ζ(3)', Acta Arith. 97 (2001) 269-293.
16. T. RIVOAL, 'La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs', C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 267-270.
17. T. RIVOAL, 'Propriétés diophantiennes des valeurs de la fonction zêta de Riemann aux entiers impairs', Thèse de Doctorat, Université de Caen, 2001.
18. T. RIVOAL and W. ZUDILIN, 'Diophantine properties of numbers related to Catalan's constant', Math. Ann. 326 (2003) 705-721.
19. 4', Preprint, M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, 2002.
20. O. N. VASILENKO, 'Certain formulae for values of the Riemann zeta-function at integral points', Number theory and its applications. Proceedings of the Science-Theoretic Conference (Tashkent, 26-28 September 1990) 27.
21. D. V. VASILYEV, 'On small linear forms for the values of the Riemann zeta-function at odd points', Preprint 1 (558), Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, 2001.
22. C. VIOLA, 'Birational transformations and values of the Riemann zeta-function', J. Théor. Nombres Bordeaux 15 (2003) 561-592 (Actes des 12èmes Rencontres Arithmétiques de Caen (29-30 June 2001)).
23. F. J. W. WHIPPLE, 'On well-poised series, generalized hypergeometric series having parameters in pairs, each pair with the same sum', Proc. London Math. Soc. (2) 24 (1926) 247-263.
24. F. J. W. WHIPPLE, 'Some transformations of generalized hypergeometric series', Proc. London Math. Soc. (2) 26 (1927) 257-272.
25. E. T. WHITTAKER and G. N. WATSON, A course of modern analysis (Cambridge University Press, 1927).
26. W. ZUDILIN, 'Very well-poised hypergeometric series and multiple integrals', Uspelchi Mat. Nauk 57 (2002) 177-178.
27. W. ZUDILIN, 'Well-poised hypergeometric service for diophantine problems of zeta values', J. Théor. Nombres Bordeaux 15 (2003) 593-626 (Actes des 12èmes Rencontres Arithmétiques de Caen (29-30 June 2001)).
28. W. ZUDILIN, 'Arithmetic of linear forms involving odd zeta values', J. Théor. Nombres Bordeaux, to appear (e-print math.NT/0206176).