Discrete Painlevé II equation over finite fields

Discrete Painlevé II equation over finite fields

We investigate the discrete Painlevé II equation over finite fields. We treat it over local fields and observe that it has a property that is similar to the good reduction over finite fields. We can use this property, which seems to be an arithmetic analogue of singularity confinement, to avoid the...

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Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-08, Vol.45 (34), p.342001-1-342001-8
Hauptverfasser: Kanki, M, Mada, J, Tamizhmani, K M, Tokihiro, T
Format: Artikel
Sprache:eng
Schlagworte:
Analogue
Arithmetic
Confinement
discrete integrable equation
discrete Painleve equation
Exact sciences and technology
finite field
good reduction
Mathematical analysis
Physics
Reduction
Singularities
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Zusammenfassung:We investigate the discrete Painlevé II equation over finite fields. We treat it over local fields and observe that it has a property that is similar to the good reduction over finite fields. We can use this property, which seems to be an arithmetic analogue of singularity confinement, to avoid the indeterminacy of the equations over finite fields and to obtain special solutions from those defined originally over fields of characteristic zero.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/34/342001