Approximations to q-logarithms and q-dilogarithms, with applications to q-zeta values

Journal of Mathematical Sciences

Volumn 137, Issue 2, 2006, Pages 4673-4683

  Zudilin, W ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746276949     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-006-0263-y     Document Type: Article

References (14)

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3. n + r))," J. Number Theory, 37, 253-259 (1991).
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5. P. Bundschuh and K. Väänänen, "Linear independence of q-analogues of certain classical constants," Results Math. (2005), to appear.
6. P. Bundschuh and W. Zudilin, "Rational approximations to a q-analogue of π and some other q-series," in: A 70th Birthday Conference in Honor of Wolfgang M. Schmidt (November 2003, Vienna), Berlin, Springer-Verlag (2005), to appear.
7. P. Erdos, "On arithmetical properties of Lambert series," J. Indiana Math. Soc., 12, 63-66 (1948).
8. G. Gasper and M. Rahman, "Basic hypergeometric series," Encyclopedia, Mathematics, 35, Cambridge Univ. Press, Cambridge (1990).
9. M. Hata, "Rational approximations to π and some other numbers," Acta Arith., 63, No. 4, 335-349 (1993).
10. T. Matalo-aho, K. Väänänen, and W. Zudilin, "New irrationality measures for q-logarithms," Math. Comput. (2004), submitted.
11. q(2), Manuscript (2004).
12. W. Zudilin, "On the irrationality measure for a q-analog of ζ(2)," Mat. 56., 93, No. 8, 49-70 (2002).
13. W. Zudilin, "Diophantine problems for q-zeta values," Mat. Zametki, 72, No. 6, 936-940 (2002).
14. W. Zudilin, "Heine's basic transform and a permutation group for q-harmonic series," Acta Arith., 111, No. 2, 153-164 (2004).