IDENTITIES FOR DIRICHLET AND LAMBERT-TYPE SERIES ARISING FROM THE NUMBERS OF A CERTAIN SPECIAL WORD

Applicable Analysis and Discrete Mathematics

article

Irem Kucukoglu¹  Yilmaz Simsek² 

[1] Department of Engineering Fundamental Sciences, Faculty of Engineering, Alanya Alaaddin Keykubat University TR-07425 Antalya;Department of Mathematics, Faculty of Science University of Akdeniz TR-07058 Antalya

关键词: Number-theoretic function;    Lyndon words;    Apostol-Bernoulli numbers;    Lambert Series;    Dirichlet series;   

DOI  :  10.2298/AADM181214033K

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

The goal of this paper is to give several new Dirichlet-type series associatedwith the Riemann zeta function, the polylogarithm function, and also thenumbers of necklaces and Lyndon words. By applying Dirichlet convolutionformula to number-theoretic functions related to these series, various novelidentities and relations are derived. Moreover, some new formulas relatedto Bernoulli-type numbers and polynomials obtain from generating functionsand these Dirichlet-type series. Finally, several relations among the Fourierexpansion of Eisenstein series, the Lambert series and the number-theoreticfunctions are given.

【 授权许可】

Unknown