$F_q$-Linear Calculus over Function Fields

Anatoly N. Kochubei

paper

$F_{q}$ -Linear Calculus over Function Fields

arXiv:math/9807075

Abstract

We define analogues of higher derivatives for $F_{q}$ -linear functions over the field of formal Laurent series with coefficients in $F_{q}$ . This results in a formula for Taylor coefficients of a $F_{q}$ -linear holomorphic function, a definition of classes of $F_{q}$ -linear smooth functions which are characterized in terms of coefficients of their Fourier-Carlitz expansions. A Volkenborn-type integration theory for $F_{q}$ -linear functions is developed; in particular, an integral representation of the Carlitz logarithm is obtained.

18 pages, LaTex-2e, to appear in Journal of Number Theory

Fq​-Linear Calculus over Function Fields

Abstract

$F_{q}$ -Linear Calculus over Function Fields