Study on irreducibility of algebraic difference equations and differential transcendence of solutions
Project/Area Number |
26800049
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Yamagata University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2018-03-31
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Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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Keywords | 差分方程式 / 差分代数 / 既約性 / 超超越性 / 差分リッカチ方程式 / qエアリー方程式 / 可解性 / 超越数論 / マーラー関数 |
Outline of Final Research Achievements |
We say that a function is differentially transcendental when it does not satisfy any algebraic differential equation. There are various studies on differential transcendence of functions satisfying difference equations. O. Hoelder's study on Gamma function is typical. In 1905, H. Tietze studied differential transcendence of solutions of difference Riccati equations, and obtained a sufficient condition. In this study, H. Tietze's result is made purely algebraic, and applicable to difference Riccati equations with other transforming operators such as one of q-difference, Mahler type, etc. As an application, it is seen that a solution of q-Airy equation is differentially transcendental when q is not a root of unity. The theory and the method for proving irreducibility of q-Painleve euqations are found to be applicable to a d-Painleve equation.
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Report
(5 results)
Research Products
(9 results)