Unified presentation of p-adic L-functions associated with unification of the special numbers
- 135 Downloads
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 , 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.
Key words and phrasesBernoulli 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
Mathematics Subject Classification11B68 11S40 11S80 11M99 30B50 44A05
Unable to display preview. Download preview PDF.
- 8.K. Iwasawa, Lectures on p-adic L-function, Princeton Univ. Press (1972).Google Scholar
- 16.H. Ozden, Unification of generating function of the Bernoulli, Euler and Genocchi numbers and polynomials, Amer. Inst. Phys. Conf. Proc., 1281 (2010), 1125–1128.Google Scholar
- 20.H. Ozden and Y. Simsek, Unified representation of the family of L-functions, J. Inequalities Appl., 64 (2013).Google Scholar
- 32.H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers (Amsterdam, London, New York, 2012).Google Scholar
- 35.L. C. Washington, Introduction to Cyclotomic Fields, Springer-Verlag (1st ed.), (1982).Google Scholar