Cauchy-Carlitz numbers
Number Theory
2021-03-01 v3
Abstract
In 1935 Carlitz introduced Bernoulli-Carlitz numbers as analogues of Bernoulli numbers for the rational function field . 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 . Several new identities are also obtained by using Hasse-Teichim\"uller derivatives.
Cite
@article{arxiv.1508.01858,
title = {Cauchy-Carlitz numbers},
author = {Hajime Kaneko and Takao Komatsu},
journal= {arXiv preprint arXiv:1508.01858},
year = {2021}
}