Twisted p-adic (h, q)-L-functions

Simsek Y.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, cilt.59, sa.6, ss.2097-2110, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 6
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.camwa.2009.12.015
  • Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2097-2110
  • Anahtar Kelimeler: q-Bernoulli numbers and polynomials, Twisted q-Bernoulli numbers and polynomials, q-zeta function, p-adic L-function, Twisted q-zeta function, Twisted q-L-function, q-Volkenborn integral, BERNOULLI NUMBERS, Q-ANALOG, ZETA-FUNCTIONS, L-SERIES, POLYNOMIALS, INTEGRALS, EULER, CONSTANTS, INTEGERS, BEHAVIOR
  • Akdeniz Üniversitesi Adresli: Evet

Özet

By using the q-Volkenborn integral on Z(p), in Simsek (2006) [33] and Simsek (2007) [34], generating functions for the (h, q)-Bernoulli polynomials and numbers were defined. By using these functions, we define a new twisted (h, q)-partial zeta function which interpolates the twisted (h, q)-Bernoulli polynomials and generalized twisted (h, q)Bernoulli numbers at negative integers. We give a relation between twisted (h, q)-partial zeta functions and the twisted (h, q)-two-variable L-function. We find the value of this function at s = 0. We also find the residue of this function at s = 1. We construct a p-adic twisted (h, q)-L-function which interpolates the twisted (h, q)-Bernoulli polynomials: