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

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Kucukoglu I., ŞİMŞEK Y.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, cilt.13, sa.3, ss.787-804, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2298/aadm181214033k
  • Dergi Adı: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.787-804
  • Anahtar Kelimeler: Apostol-Bernoulli numbers, Dirichlet convolution, Dirichlet series, Generating function, Lambert series, Polylogarithm, Lyndon words, Necklace polynomial, Number-theoretic function, BERNOULLI, EULER
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.