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

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
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References:

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