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arXiv · 1206.4456

Discrete Painleve II equation over finite fields

Masataka Kanki·Jun Mada·K. M. Tamizhmani·Tetsuji Tokihiro
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Abstract

We investigate the discrete Painleve 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.

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Masataka Kanki, Jun Mada, K. M. Tamizhmani, Tetsuji Tokihiro. 2012-06-20. Discrete Painleve II equation over finite fields. https://doi.org/10.1088/1751-8113/45/34/342001

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