8 papers · 1 filter
Hypergeometric Functions and Carlitz Differential Equations over Function Fields
Anatoly N. Kochubei
The paper is a survey of recent results in analysis of additive functions over function fields motivated by applications to various classes of special functions including Thakur's…
Polylogarithms and a Zeta Function for Finite Places of a Function Field
Anatoly N. Kochubei
We introduce and study new versions of polylogarithms and a zeta function on a completion of at a finite place. The construction is based on the use of the Carlit…
Umbral Calculus in Positive Characteristic
Anatoly N. Kochubei
An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in…
Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field
Anatoly N. Kochubei
In earlier papers the author studied some classes of equations with Carlitz derivatives for -linear functions, which are the natural function field counterparts of lin…
Differential Equations for -Linear Functions, II: Regular Singularity
Anatoly N. Kochubei
We study some classes of equations with Carlitz derivatives for -linear functions, which are the natural function field counterparts of linear ordinary differential equations…
Analysis and Probability over Infinite Extensions of a Local Field, II: A Multiplicative Theory
Anatoly N. Kochubei
Let be a projective limit, with respect to the renormalized norm mappings, of the groups of principal units corresponding to a strictly increasing sequence of finite separable…