Analytic continuation of the Lucas zeta and L-functions

被引：13

作者：

Kamano, Ken ^{[1
]}

机构：

[1] Osaka Inst Technol, Dept Math, Asahi, Osaka 5358585, Japan

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2013年 / 24卷 / 03期

关键词：

Lucas sequences; The Fibonacci zeta function; Dirichlet's L-functions; FIBONACCI NUMBERS; RECIPROCAL SUMS;

D O I：

10.1016/j.indag.2013.04.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Lucas zeta function defined by using the Lucas sequence which is a generalization of the Fibonacci sequence. This zeta function can be meromorphically continued to the whole complex plane, and in a special case, it has "trivial zeros" like the Riemann zeta function. Analogues of Dirichlet's L-functions are also investigated. (C) 2013 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：637 / 646

页数：10

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