UNIFIED PRESENTATION OF p-ADIC L-FUNCTIONS ASSOCIATED WITH UNIFICATION OF THE SPECIAL NUMBERS

Ozden H., ŞİMŞEK Y.

ACTA MATHEMATICA HUNGARICA, cilt.144, sa.2, ss.515-529, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 144 Sayı: 2
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10474-014-0446-9
  • Dergi Adı: ACTA MATHEMATICA HUNGARICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.515-529
  • Anahtar Kelimeler: Bernoulli number and polynomial, Euler number and polynomial, Genocchi number and polynomial, Riemann and Hurwitz (or generalized) zeta function, partial zeta type function, p-adic function, p-adic L-function, partial differential equation (PDE), generating function, GENERATING-FUNCTIONS, Q-ANALOG, EULER, BERNOULLI, POLYNOMIALS, BEHAVIOR, (H, EXTENSION, FAMILIES, SERIES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

By using partial differential equations (PDEs) of the generating functions for the unification of the Bernoulli, Euler and Genocchi polynomials and numbers, we derive many new identities and recurrence relations for these polynomials and numbers. In [33], Srivastava et al. defined a unified presentation of certain meromorphic functions related to the families of the partial zeta type functions. By using these functions, we construct p-adic functions which are related to the partial zeta type functions. By applying these p-adic function, we construct unified presentation of p-adic L-functions. These functions give us generalization of the Kubota-Leopoldt p-adic L-functions, which are related to the Bernoulli numbers and the other p-adic L-functions, which are related to the Euler numbers and polynomials. We also give some remarks and comments on these functions.