Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions. (English) Zbl 1173.11064

Simsek, Yilmaz

Adv. Stud. Contemp. Math., Kyungshang 16, No. 2, 251-278 (2008).

The author continues his long series of papers around Bernoulli numbers and polynomials, Riemann’s and Hurwitz’s zeta function and Dirichlet’s \(L\)-functions, in particular their twisted and \(q\)-twisted versions. (Here \(q\) denotes either a complex or a \(p\)-adic number satisfying certain conditions.) The main purpose of the present article is, as the author says in the abstract, to study generating functions of twisted and \(q\)-twisted Bernoulli numbers and polynomials. The functions mentioned above are constructed from these by using the Mellin transform. The article seems to be partly of a survey type with numerous references to previous results, and it is not always clear what is new.
There are many lapses and some confusing statements showing that the author should have checked his text more carefully.

Reviewer: Tauno Metsänkylä (Turku)

MSC:

11S40	Zeta functions and \(L\)-functions
11B68	Bernoulli and Euler numbers and polynomials
11S80	Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
44A20	Integral transforms of special functions

Keywords:

\(p\)-adic \(L\)-functions; twisted \(L\)-functions; zeta functions; Bernoulli numbers and polynomials; transforms of special functions