Quasi-Holonomic Modules in Positive Characteristic
Abstract
Description
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.
20 pages. Version 3: everywhere, including the title, the term "quasi-holonomic" is used instead of "holonomic"; other minor changes have been made; to appear in the Journal of Algebra
20 pages. Version 3: everywhere, including the title, the term "quasi-holonomic" is used instead of "holonomic"; other minor changes have been made; to appear in the Journal of Algebra