Analytic continuation of the multiple Fibonacci zeta functions

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2018-06-01 DOI:10.3792/PJAA.94.64

S. S. Rout, N. K. Meher

引用次数: 6

Abstract

: In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.

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多重斐波那契函数的解析延拓

在本文中，我们证明了深度为2的多个Fibonacci zeta函数的亚纯延拓，其中fn是第n个Fibonacci数，Re ð s 1 Þ > 0, Re ð s 2 Þ > 0。我们计算了它的极点及其残数的完整列表。我们也证明了多个Fibonacci zeta值在负整数参数上是有理数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.