Küçükoğlu, İremŞimşek, Yılmaz2021-02-192021-02-1920191452-8630https://doi.org/10.2298/AADM181214033Khttps://hdl.handle.net/20.500.12868/508Mediterranean International Conference of Pure and Applied Mathematics and Related Areas -- OCT 26-29, 2018 -- Antalya, TURKEYThe 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.eninfo:eu-repo/semantics/openAccessApostol-Bernoulli numbersDirichlet convolutionDirichlet seriesGenerating functionLambert seriesPolylogarithmLyndon wordsNecklace polynomialNumber-theoretic functionConference Object10.2298/AADM181214033K133787804Q1WOS:000503720000009N/A