2013 Fiscal Year Final Research Report
Irreducibility and hypertranscendence of non-linear difference equations
| Project/Area Number |
24840005
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | 離散パンルヴェ方程式 / 既約性 / 超越性 / 代数的差分方程式 |
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| Research Abstract |
There are special second-order algebraic difference equations called discrete Painleve equations. The equation called d-Painleve equation of type D7(1) is one of them. Its irreducibility in the sense of decomposable extension was proved. The irreducibility implies that the transcendental function solution cannot be built from rational functions by reiterating algebraic operations and the taking of solutions of linear difference equations or first-order algebraic difference equations. A standard form of difference Riccati equations for any transforming operator was also studied.
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