Cauchy-Carlitz numbers

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• 作者：Hajime Kaneko^a ; ^b ; ^{kanekoha@math.tsukuba.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Takao Komatsu^c ; ^{komatsu@whu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bernoulli&ndash ; Carlitz numbers ; Cauchy&ndash ; Carlitz numbers ; Stirling&ndash ; Carlitz numbers ; Hasse&ndash ; Teichmü ; ller derivatives
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：163
• 期：Complete
• 页码：238-254
• 全文大小：315 K

文摘

In 1935 Carlitz introduced Bernoulli–Carlitz numbers as analogues of Bernoulli numbers for the rational function field F_r(T)${\mathbb{F}}_r(T)$. 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 F_r(T)${\mathbb{F}}_r(T)$. Several new identities are also obtained by using Hasse–Teichmüller derivatives.