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

Sangtae Jeong
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Abstract

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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Sangtae Jeong. 2000-03-13. A comparison of the Carlitz and digit derivatives bases in function field arithmetic. https://arxiv.org/abs/math/0003243

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