Arithmetical properties of solutions of linear second order \(q\)-difference equations. (English) Zbl 1132.11334
Kanemitsu, Shigeru (ed.) et al., Number theoretic methods. Future trends. Proceedings of the 2nd China-Japan seminar, Iizuka, Fukuoka, Japan, March 12–16, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1080-X/hbk). Dev. Math. 8, 15-29 (2002).
Summary: A linear dependence measure is obtained for the values \(F(t)\) and \(F(qt)\) of solutions \(F(z)\) of linear second order \(q\)-difference equations. From the result, an irrationality measure for certain continued fractions is derived.
For the entire collection see [Zbl 1007.00028].
For the entire collection see [Zbl 1007.00028].
MSC:
| 11J82 | Measures of irrationality and of transcendence |
| 11J70 | Continued fractions and generalizations |
| 39A13 | Difference equations, scaling (\(q\)-differences) |
