2002 Fiscal Year Final Research Report Summary
A Research on Linear Independence of Special Values of qFunctions
Project/Area Number 
13640007

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Gunma University 
Principal Investigator 
AMOU Masaaki Gunma University, Faculty of Engineering. Associate Professor > 群馬大学, 工学部, 助教授 (60201901)

CoInvestigator(Kenkyūbuntansha) 
AMANO Kazuo Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (90137795)
IKEHATA Masaru Gunma University, Faculty of Engineering, Associate Professor, 工学部, 教授 (90202910)
SAITOU Saburho Gunma University, Faculty of Engineering. Professor, 工学部, 教授 (10110397)
KATSURADA Masanori Keio University, Faculty of Economics, Professor, 経済学部, 教授 (90224485)
SATO Hisashi Gunma University, Faculty of Engineering, Assistant, 工学部, 助手 (60008513)

Project Period (FY) 
2001 – 2002

Keywords  q Function / qHypergeometric Sereis / Irrationality Measure / Linear Independence / Rationality Criterion / Theta Series / Linear Recurrence Sequence 
Research Abstract 
We have studied linear independence of special values of certain qfunctions and obtained the following results. 1. We proved linear independence of the values of functions satisfying linear second order qdifference equations. The head investigator published a paper on the result (Proceedings of the ChinaJapan Seminar, in press) with Prof. T. Matalaaho (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. Matalaaho twice (AugustSeptember, 2001 ; AugustSeptember, 2002), which was very important for the present research.

Research Products
(12 results)