Fq-linear calculus over function fields (1999)
| Venue: | J. Number Theory |
| Citations: | 8 - 8 self |
BibTeX
@ARTICLE{Kochubei99fq-linearcalculus,
author = {Anatoly N. Kochubei},
title = {Fq-linear calculus over function fields},
journal = {J. Number Theory},
year = {1999},
pages = {281--300}
}
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Abstract
We define analogues of higher derivatives for Fq-linear functions over the field of formal Laurent series with coefficients in Fq. This results in a formula for Taylor coefficients of a Fq-linear holomorphic function, a definition of classes of Fq-linear smooth functions which are characterized in terms of coefficients of their Fourier-Carlitz expansions. A Volkenborn-type integration theory for Fq-linear functions is developed; in particular, an integral representation of the Carlitz logarithm is obtained. Key words: Fq-linear function; Carlitz basis; Carlitz logarithm; Volkenborn integral; difference operator; Bargmann-Fock representation.
