A Research on Linear Independence of Special Values of q-Functions

点击翻译按钮获取中文摘要

We have studied linear independence of special values of certain q-functions and obtained the following results.1. We proved linear independence of the values of functions satisfying linear second order q-difference equations. The head investigator published a paper on the result (Proceedings of the China-Japan Seminar, in press) with Prof. T. Matala-aho (University of Oulu).2. We considered the values of power series introduced by Bezivin and proved linear independence of them qualitatively, which generalized earlier results obtained by Bezivin. The head investigator published a paper on the result (The Ramanujan J., in press) with Prof. K. Vaananen (University of Oulu, a investigator from abroad).3. We considered the values of generalized Tschakaloff series and obtained quantitative irrationality and linear independence results. The head investigator published a paper on the result (J. Number Theory, in press) with Prof. M. Katsurada (Keio University, one of the investigators).4. We proved linear independence of the values of theta series. The head investigator submitted a paper on the result with Prof. Vaananen.By the support of the grant concerned, the head investigator visited Prof. Vaananen and Prof. Matala-aho twice (August-September, 2001 ; August-September, 2002), which was very important for the present research.