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Fq-Linear Calculus over Function Fields

✍ Scribed by Anatoly N. Kochubei

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
150 KB
Volume
76
Category
Article
ISSN
0022-314X

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✦ Synopsis

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.

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