Congruences for generalized \(q\)-Bernoulli polynomials. (English) Zbl 1246.11045

Cenkci, Mehmet; Kurt, Veli

J. Inequal. Appl. 2008, Article ID 270713, 19 p. (2008).

Summary: We give some further properties of the \(p\)-adic \(q\)-\(L\)-function of two variables, which has recently been constructed by T. Kim [Russ. J. Math. Phys. 12, No. 2, 186–196 (2005; Zbl 1190.11049)] and the first author [\(p\)-adic \(q\)-\(L\)-function of two variables, Ph.D. thesis, Department of Mathematics, Akdeniz University, Antalya, Turkey (2006)]. One of the applications of these properties yields general classes of congruences for generalized \(q\)-Bernoulli polynomials, which are \(q\)-extensions of the classes for generalized Bernoulli numbers and polynomials given by G. J. Fox [Enseign. Math., II. Sér. 46, No. 3-4, 225–278 (2000; Zbl 0999.11073)], H. S. Gunaratne [CMS Conf. Proc. 15, 209–214 (1995; Zbl 0843.11012)], and P. T. Young [J. Number Theory 78, No. 2, 204–227 (1999; Zbl 0939.11014), Acta Arith. 99, No. 3, 277–288 (2001; Zbl 0982.11008)].

MSC:

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

Citations:

Zbl 1190.11049; Zbl 0999.11073; Zbl 0843.11012; Zbl 0939.11014; Zbl 0982.11008

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