Research Article

Appell-Carlitz numbers

Published in: Quaestiones Mathematicae
Volume 45 , issue 12 , 2022 , pages: 1877–1893

DOI: 10.2989/16073606.2021.1977412

Author(s): Su Hu South China University of Technology, China , Min-Soo Kim Kyungnam University, Republic of Korea

Keywords: 11R58 , 11R60 , 11B68 , Appell-Carlitz numbers , explicit expressions , determinants , recurrence relations

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Abstract

In this paper, we introduce the concept of the (higher order) Appell-Carlitz numbers which unifies the definitions of several special numbers in positive characteristic, such as the Bernoulli-Carlitz numbers and the Cauchy-Carlitz numbers. Their generating function is named Hurwitz series in the function field arithmetic ([11, p. 352, Definition 9.1.4]). By using Hasse-Teichmüller derivatives, we also obtain several properties of the (higher order) Appell-Carlitz numbers, including a recurrence formula, two closed forms expressions, and a determinant expression.

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