Arithmetical properties of hypergeometric Bernoulli numbers

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• 作者：Daniel Berhanu^a ; ^{berhanu@mathematik.uni-kl.de} ; Hunduma Legesse^b ; ^{hunduma.legesse@aau.edu.et}
• 关键词：Hypergeometric Bernoulli numbers ; Hypergeometric zeta function ; Carlitz numbers
• 刊名：Indagationes Mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：28
• 期：1
• 页码：84-90
• 全文大小：184 K
• 卷排序：28

文摘

In a recent paper, Byrnes et al. (2014) have developed some recurrence relations for the hypergeometric zeta functions. Moreover, the authors made two conjectures for arithmetical properties of the denominators of the reduced fraction of the hypergeometric Bernoulli numbers. In this paper, we prove these conjectures using some recurrence relations. Furthermore, we assert that the above properties hold for both Carlitz and Howard numbers.