Bulletin of the Belgian Mathematical Society - Simon Stevin

Evolution Equations and Functions of Hypergeometric Type over Fields of Positive Characteristic

Anatoly N. Kochubei

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Abstract

We consider a class of partial differential equations with Carlitz derivatives over a local field of positive characteristic, for which an analog of the Cauchy problem is well-posed. Equations of such type correspond to quasi-holonomic modules over the ring of differential operators with Carlitz derivatives. The above class of equations includes some equations of hypergeometric type. Building on the work of Thakur, we develop his notion of the hypergeometric function of the first kind (whose parameters belonged initially to $\mathbb Z$) in such a way that it becomes fully an object of the function field arithmetic, with the variable, parameters and values from the field of positive characteristic.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 5 (2007), 947-959.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1197908905

Mathematical Reviews number (MathSciNet)
MR2378999

Zentralblatt MATH identifier
1197.12004

Subjects
Primary: 12H99: None of the above, but in this section 33E50: Special functions in characteristic $p$ (gamma functions, etc.)
Secondary: 16S32: Rings of differential operators [See also 13N10, 32C38]

Keywords
$F_q$-linear function quasi-holonomic module hypergeometric function Carlitz derivative

Citation

Kochubei, Anatoly N. Evolution Equations and Functions of Hypergeometric Type over Fields of Positive Characteristic. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 5, 947--959. https://projecteuclid.org/euclid.bbms/1197908905


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