Cauchy-Carlitz numbers

Hajime Kaneko; Takao Komatsu

doi:10.1016/j.jnt.2015.11.019

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arXiv · 1508.01858

Cauchy-Carlitz numbers

Hajime Kaneko·Takao Komatsu

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Abstract

In 1935 Carlitz introduced Bernoulli-Carlitz numbers as analogues of Bernoulli numbers for the rational function field $\mathbb F_r(T)$. In this paper, we introduce Cauchy-Carlitz numbers as analogues of Cauchy numbers. By using Stirling-Carlitz numbers, we give their arithmetical and combinatorial properties and relations with Bernoulli-Carlitz numbers for $\mathbb F_r(T)$. Several new identities are also obtained by using Hasse-Teichimüller derivatives.

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Hajime Kaneko, Takao Komatsu. 2015-11-04. Cauchy-Carlitz numbers. https://doi.org/10.1016/j.jnt.2015.11.019

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