Analytic continuation of the multiple Lucas zeta functions

被引：6

作者：

Meher, Nabin Kumar ^{[1
]}

Rout, Sudhansu Sekhar ^{[2
]}

机构：

[1] Harish Chandra Res Inst HBNI, Chhatnag Rd, Jhunsi 211019, India

[2] Inst Math & Applicat, Bhubaneswar 751029, India

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 468卷 / 02期

关键词：

Analytic continuation; Multiple Lucas zeta function; Lucas sequence; Residues and poles; FIBONACCI NUMBERS; RECIPROCAL SUMS;

D O I：

10.1016/j.jmaa.2018.08.063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is a continuation of our previous paper [7], in which multiple Fibonacci zeta functions of depth 2 have been studied. In this article, we consider more general situation. In particular, we prove the meromorphic continuation of the multiple Lucas zeta functions of depth d: Sigma(0 < n1 < ... < nd) 1/U-n1(s1) ... U-nd(sd), where U-n, is the n-th Lucas number of first kind and Sigma(d)(i=j) Re(s(i)) > 0 for 1 <= j <= d. We compute a complete list of poles and their residues. We also prove that the multiple Lucas zeta values at negative integer arguments are rational. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1115 / 1130

页数：16

共 50 条

[11] Analytic continuation of multiple q-zeta functions and their values at negative integers
Kim, T
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2004, 11 (01) : 71 - 76
[12] The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions I
Matsumoto, K
[J]. JOURNAL OF NUMBER THEORY, 2003, 101 (02) : 223 - 243
[13] Analytic continuation of multiple zeta-functions and their values at non-positive integers
Akiyama, S
Egami, S
Tanigawa, Y
[J]. ACTA ARITHMETICA, 2001, 98 (02) : 107 - 116
[14] ANALYTIC CONTINUATION OF PARTIAL ZETA-FUNCTIONS OF ARITHMETIC ORDERS
BUSHNELL, CJ
REINER, I
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1984, 349 : 160 - 178
[15] Expanding maps on cantor sets and analytic continuation of zeta functions
Naud, F
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2005, 38 (01): : 116 - 153
[16] ANALYTIC CONTINUATION OF MULTIPLE ZETA-FUNCTIONS AND THE ASYMPTOTIC BEHAVIOR AT NON-POSITIVE INTEGERS
Onozuka, Tomokazu
[J]. FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2013, 49 (02) : 331 - 348
[17] Analytic continuation for multiple zeta values using symbolic representations
Jiu, Lin
Vignat, Christophe
Wakhare, Tanay
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2020, 16 (03) : 579 - 602
[18] ON AN ANALYTIC CONTINUATION OF ZETA(S)
BALASUBRAMANIAN, R
RAMACHANDRA, K
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1987, 18 (09): : 790 - 793
[19] ON THE ANALYTIC CONTINUATION OF CERTAIN ZETA-FUNCTIONS AND A FUNDAMENTAL THEOREM ON SIMPLE ALGEBRAS
EICHLER, MME
[J]. ANNALS OF MATHEMATICS, 1949, 50 (04) : 816 - 826
[20] CONTINUATION OF ANALYTIC FUNCTIONS
SHAPIRO, HS
KENNEDY, PB
[J]. AMERICAN MATHEMATICAL MONTHLY, 1966, 73 (01): : 94 - &

← 1 2 3 4 5 →