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
收藏
页码：637 / 646
页数：10
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