Quasi-Holonomic Modules in Positive Characteristic

Details Quasi-Holonomic Modules in Positive Characteristic Quasi-Holonomic Modules in Positive Characteristic

2005-03-19

arxiv.org/abs/math/0503398v3

Mathematics

Rings and Algebras

20 pages. Version 3: everywhere, including the title, the term "quasi-holonomic" is used instead of "holonomic"; other minor c

Scientific paper

We study modules over the Carlitz ring, a counterpart of the Weyl algebra in analysis over local fields of positive characteristic. It is shown that some basic objects of function field arithmetic, like the Carlitz module, Thakur's hypergeometric polynomials, and analogs of binomial coefficients arising in the function field version of umbral calculus, generate quasi-holonomic modules. This class of modules is, in many respects, similar to the class of holonomic modules in the characteristic zero theory.

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