Diophantine problems for q-Zeta values

Mathematical Notes

Volumn 72, Issue 5-6, 2002, Pages 858-862

  Zudilin, V V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Basic hypergeometric series; Eisenstein series; Hypergeometric transformation; Irrationality measure; Zeta value

Indexed keywords

EID: 0141851247     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021450231834     Document Type: Article

References (25)

1. G. Pólya and G. Szegö, Problems and Theorems in Analysis, Pt. 2, 3rd ed., Springer-Verlag, New York, 1976.
2. M. Kaneko, N. Kurokawa, and M. Wakayama, E-print math. QA/0206171 (June 2002).
3. E. M. Nikishin, Mat. Sb. [Math. USSR-Sb.], 109 (151) (1979), no. 3 (7), 410-417.
4. L. A. Gutnik, Acta Arith., 42 (1983), no. 3, 255-264.
5. Yu. V. Nesterenko, Mat. Zametki [Math. Notes], 59 (1996), no. 6, 865-880.
6. G. V. Chudnovsky, Ann. of Math. (2), 117 (1983), no. 2, 325-382.
7. E. A. Rukhadze, Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] (1987), no. 6, 25-29.
8. M. Hata, J. Reine Angew. Math., 407 (1990), no. 1, 99-125.
9. G. Rhin and C. Viola, Acta Arith., 77 (1996), no. 1, 23-56.
10. G. Rhin and C. Viola, Acta Arith., 97 (2001), no. 3, 269-293.
11. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Cambridge Univ. Press, Cambridge, 1990.
12. P. Bundschuh and K. Väänänen, Compositio Math., 91 (1994), 175-199.
13. Assche W. Van, The Ramanujan J., 5 (2001), no. 3, 295-310.
14. V. V. Zudilin (W. Zudilin), Manuscripta Math., 107 (2002), no. 4, 463-477.
15. E. Heine, J. Reine Angew. Math., 34 (1847), 285-328.
16. V. V. Zudilin (W. Zudilin), E-print math. NT/0206176 (August 2001).
17. V. V. Zudilin, Mat. Sb. [Russian Acad. Sci. Sb. Math.], 193 (2002), no. 8, 49-70.
18. Yu. V. Nesterenko, Mat. Sb. [Russian Acad. Sci. Sb. Math.], 187 (1996), no. 9, 65-96.
19. R. Apéry, Astérisque, 61 (1979), 11-13.
20. R. Askey, Appl. Anal., 8 (1978), 125-141.
21. H. Exton, q-Hypergeometric Functions and Applications, Ellis Horwood Ser. Math. Appl., Ellis Horwood, Chichester, 1983.
22. F. Lindemann, Math. Annalen, 20 (1882), 213-225.
23. G. E. Andrews, R. Lewis, and Z.-G. Liu, Bull. London Math. Soc., 33 (2001), 25-31.
24. T. Matala-aho and K. Väänänen, Bull. Austral. Math. Soc., 58 (1998), 15-31.
25. M. Waldschmidt, J. Théorie des nombres de Bordeaux, 12 (2000), 581-595.