Open Access
December 2007 Evolution Equations and Functions of Hypergeometric Type over Fields of Positive Characteristic
Anatoly N. Kochubei
Bull. Belg. Math. Soc. Simon Stevin 14(5): 947-959 (December 2007). DOI: 10.36045/bbms/1197908905


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.


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Anatoly N. Kochubei. "Evolution Equations and Functions of Hypergeometric Type over Fields of Positive Characteristic." Bull. Belg. Math. Soc. Simon Stevin 14 (5) 947 - 959, December 2007.


Published: December 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1197.12004
MathSciNet: MR2378999
Digital Object Identifier: 10.36045/bbms/1197908905

Primary: 12H99 , 33E50
Secondary: 16S32

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

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 5 • December 2007
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