A two-variable dirichlet series and its applications

Cenkci M., Unal A.

QUAESTIONES MATHEMATICAE, cilt.44, sa.12, ss.1661-1679, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 12
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2989/16073606.2020.1818644
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1661-1679
  • Anahtar Kelimeler: Dirichlet series, zeta functions, Bernoulli numbers, DOUBLE ZETA, ANALYTIC CONTINUATION, EULER, IDENTITIES, BERNOULLI, FORMULA, VALUES, SUMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We define a two-variable Dirichlet series associated with two arithmetic functions, which is related to the Riemann zeta function, the DirichletL-function, the Dirichlet series associated to the harmonic numbers, and truncated multiple zeta functions. Using the periodic Euler-Maclaurin summation formula, we obtain a representation in terms of an ordinary Dirichlet series, which leads to the explicit evaluation of its values at nonpositive integers. We also find a reciprocity formula, which provides some symmetric formulas involving Bernoulli and associated numbers.