IDENTITIES FOR DIRICHLET AND LAMBERT-TYPE SERIES ARISING FROM THE NUMBERS OF A CERTAIN SPECIAL WORD
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, vol.13, no.3, pp.787-804, 2019 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 13 Issue: 3
- Publication Date: 2019
- Doi Number: 10.2298/aadm181214033k
- Journal Name: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.787-804
- Keywords: Apostol-Bernoulli numbers, Dirichlet convolution, Dirichlet series, Generating function, Lambert series, Polylogarithm, Lyndon words, Necklace polynomial, Number-theoretic function, BERNOULLI, EULER
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
The goal of this paper is to give several new Dirichlet-type series associated with the Riemann zeta function, the polylogarithm function, and also the numbers of necklaces and Lyndon words. By applying Dirichlet convolution formula to number-theoretic functions related to these series, various novel identities and relations are derived. Moreover, some new formulas related to Bernoulli-type numbers and polynomials obtain from generating functions and these Dirichlet-type series. Finally, several relations among the Fourier expansion of Eisenstein series, the Lambert series and the number-theoretic functions are given.