A Research on the Theory of Irrational Numbers for q-Functions
| Project/Area Number |
15540006
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Gunma University |
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Principal Investigator |
AMOU Masaaki Gunma University, Faculty of Engineering, Professor, 工学部, 助教授 (60201901)
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| Co-Investigator(Kenkyū-buntansha) |
SAITOU Saburho Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (10110397)
IKEHATA Masaru Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (90202910)
AMANO Kazuo Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (90137795)
TANUMA Kazumi Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60217156)
KATSURADA Masanori Keio University, Faculty of Economics, Professor, 経済学部, 教授 (90224485)
佐藤 久 群馬大学, 工学部, 助手 (60008513)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | q-Function / q-Difference Equation / Irrational Number / Linear Independence / Shidlovskii's Lemma |
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| Research Abstract |
We have obtained the following results mainly on the theory of irrational numbers for q-functions.
1. We estimated from above the dimension of the vector space generated by certain special values of functions satisfying linear q-difference equations with polynomial coefficients. The head investigator submitted a paper on the result with Prof.Matala-aho (University of Oulu).
2. We proved a complete analogue of Shidlovskii's lemma, both on Pade-type approximations of the first and the second kinds, for a system of q-difference equations with coefficients from rational functions. Moreover, we apply this result to get linear independence of special values of analytic functions satisfying the above system. The head investigator is preparing a paper on the result with Prof.Vaananen (University of Oulu, a investigator from abroad) and Prof.Matala-aho.
3. We convined a criterion on linear independence of functions given by Galochkin with an inductive method in Mahler functions given by Duverney-Nishioka, and created a method to obtaining a quantitative refinement of a resul of Duverney-Nishioka. The head investigator is preparing a paper on the result with Prof.Vaananen.
By the support of the grant concerned, the head investigator visited Belarus (August, 2003) and Finland (September, 2003 ; September-October, 2005), and invited Prof.Kohnen and Prof.Lasjaunias (October, 2004), which were very important for the present research.
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Report
(4 results)
Research Products
(14 results)
