Results 1 
7 of
7
Differential equations for Fqlinear functions
 J. Number Theory
"... Partially supported by CRDF under Grants UM12090 and UM12421KV02 We study some classes of equations with Carlitz derivatives for Fqlinear functions, which are the natural function field counterparts of linear ordinary differential equations with a regular singularity. In particular, an analog o ..."
Abstract

Cited by 9 (8 self)
 Add to MetaCart
Partially supported by CRDF under Grants UM12090 and UM12421KV02 We study some classes of equations with Carlitz derivatives for Fqlinear functions, which are the natural function field counterparts of linear ordinary differential equations with a regular singularity. In particular, an analog of the equation for the power function, the Fuchs and Euler type equations, and Thakur’s hypergeometric equation are considered. Some properties of the above equations are similar to the classical case while others are different. For example, a simple model equation shows a possibility of existence of a nontrivial continuous locally analytic Fqlinear solution which vanishes on an open neighbourhood of the initial point.
Umbral calculus in positive characteristic
 Adv. Appl. Math
"... Partially supported by CRDF under Grant UM12567OD03 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 the space of continuous Fqlinear functions are constructed. Key ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Partially supported by CRDF under Grant UM12567OD03 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 the space of continuous Fqlinear functions are constructed. Key words: Fqlinear function; delta operator; basic sequence; orthonormal basis 2 1
Polylogarithms and a zeta function for finite places of a function field, Contemporary Math
"... We introduce and study new versions of polylogarithms and a zeta function on a completion of Fq(x) at a finite place. The construction is based on the use of the Carlitz differential equations for Fqlinear functions. Key words: Fqlinear function; polylogarithms; zeta function 2 1 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
We introduce and study new versions of polylogarithms and a zeta function on a completion of Fq(x) at a finite place. The construction is based on the use of the Carlitz differential equations for Fqlinear functions. Key words: Fqlinear function; polylogarithms; zeta function 2 1
Holonomic Modules in Positive Characteristic
, 2005
"... Partially supported by CRDF under Grant UM12567OD03 We study modules over the WeylCarlitz 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 hypergeo ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Partially supported by CRDF under Grant UM12567OD03 We study modules over the WeylCarlitz 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 holonomic modules. Key words: Fqlinear function; holonomic module; holonomic function; Carlitz derivative 2 1
Strongly nonlinear differential equations with Carlitz derivatives over a function field
 Ukrainian Math. J
"... In earlier papers the author studied some classes of equations with Carlitz derivatives for Fqlinear functions, which are the natural function field counterparts of linear ordinary differential equations. Here we consider equations containing selfcompositions u◦u◦ · · ·◦u of the unknown function. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In earlier papers the author studied some classes of equations with Carlitz derivatives for Fqlinear functions, which are the natural function field counterparts of linear ordinary differential equations. Here we consider equations containing selfcompositions u◦u◦ · · ·◦u of the unknown function. As an algebraic background, imbeddings of the composition ring of Fqlinear holomorphic functions into skew fields are considered. 1
QuasiHolonomic Modules in Positive Characteristic
, 2006
"... Partially supported by CRDF under Grant UM12567OD03, and by the Ukrainian Foundation for Fundamental ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Partially supported by CRDF under Grant UM12567OD03, and by the Ukrainian Foundation for Fundamental
Hypergeometric Functions and Carlitz Differential Equations over Function Fields
, 2005
"... 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 hypergeometric function. We consider basic notions and results of calculus, analytic theory of differential equations wi ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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 hypergeometric function. We consider basic notions and results of calculus, analytic theory of differential equations with Carlitz derivatives (including a counterpart of regular singularity), umbral calculus, holonomic modules over the WeylCarlitz ring.