A comparison of the Carlitz and digit derivatives bases in function field arithmetic

Details A comparison of the Carlitz and digit derivatives bases in function field arithmetic A comparison of the Carlitz and digit derivatives bases in function field arithmetic

2000-03-13

arxiv.org/abs/math/0003243v1

Mathematics

Number Theory

Scientific paper

In this paper we compare several properties and constructions of the Carlitz
polynomials and digit derivatives for continuous functions on $\F_q[[T]].$ In
particular, we show a close relation between them as orthonormal bases.
Moreover, parallel to Carlitz's coefficient formula, we give the closed formula
for the expansion coefficients in terms of the digit derivatives.

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