On multi-poly-Bernoulli-Carlitz numbers
Ryotaro Harada
TL;DR
This paper introduces multi-poly-Bernoulli-Carlitz numbers as function field analogues of multi-poly-Bernoulli numbers, providing explicit formulas and exploring their connections with finite multiple zeta values in the function field setting.
Contribution
The paper defines multi-poly-Bernoulli-Carlitz numbers and derives explicit formulas involving Carlitz factorial and Stirling-Carlitz numbers, linking them to finite multiple zeta values.
Findings
Explicit formulas for multi-poly-Bernoulli-Carlitz numbers
Connections with function field analogues of multiple zeta values
New insights into function field Bernoulli-type numbers
Abstract
We introduce multi-poly-Bernoulli-Carlitz numbers, function field analogues of multi-poly-Bernoulli numbers of Imatomi-Kaneko-Takeda. We explicitly describe multi-poly-Bernoulli Carlitz numbers in terms of the Carlitz factorial and the Stirling-Carlitz numbers of the second kind and also show their relationships with function field analogues of finite multiple zeta values.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research