Cauchy-Carlitz numbers

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.

References in corpus (1)

• A Herbrand-Ribet theorem for function fields

Cited by in corpus (4)

• Remarks on hypergeometric Cauchy numbers
• Truncated Bernoulli-Carlitz and truncated Cauchy-Carlitz numbers
• Alternating variants of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p
• Appell-Carlitz numbers