|
|
|
|
Литература
|
|
| |
| 1. |
W. Van Assche, “Little $q$-Legendre polynomials and irrationality of certain Lambert
series”, Ramanujan J., 5:3 (2001), 295–310    |
| 2. |
J.-P. Bézivin, “Indépendence linéaire des valeurs des solutions transcendantes
de certaines équations fonctionelles”, Manuscripta Math., 61 (1988), 103–129 |
| 3. |
P. Borwein, “On the irrationality of $\sum(1/(q^n+r))$”, J. Number Theory, 37 (1991), 253–259 |
| 4. |
P. Bundschuh, K. Väänänen, “Arithmetical investigations of a certain infinite product”, Compositio Math., 91 (1994), 175–199 |
| 5. |
P. Bundschuh, K. Väänänen, “Linear independence of $q$-analogues of certain classical constants”, Results in Math., 2005 (to appear) |
| 6. |
P. Bundschuh, W. Zudilin, “Rational approximations to a $q$-analogue of $\pi$ and some other
$q$-series”, A 70th birthday conference in honour of Wolfgang M. Schmidt (November 2003, Vienna), Springer-Verlag, Berlin, 2005 (to appear) |
| 7. |
P. Erdős, “On arithmetical properties of Lambert series”, J. Indiana Math. Soc., 12 (1948), 63–66 |
| 8. |
G. Gasper, M. Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, 35, Cambridge Univ. Press, Cambridge, 1990 |
| 9. |
M. Hata, “Rational approximations to $\pi$ and some other numbers”, Acta Arith., 63:4 (1993), 335–349 |
| 10. |
T. Matalo-aho, K. Väänänen, W. Zudilin, “New irrationality measures for $q$-logarithms”, Math. Comput., 2004, submitted |
| 11. |
K. Postelmans, W. Van Assche, Irrationality of $\zeta_q(1)$ and $\zeta_q(2)$, Manuscript, 2004 |
| 12. |
W. Zudilin, “On the irrationality measure for a $q$-analogue of $\zeta(2)$”, Mat. Sb., 193:8 (2002), 49–70  |
| 13. |
W. Zudilin, “Diophantine problems for $q$-zeta values”, Mat. Zametki, 72:6 (2002), 936–940 |
| 14. |
W. Zudilin, “Heine's basic transform and a permutation group for $q$-harmonic series”, Acta Arith., 111:2 (2004), 153–164  |
