Congruences for Generalized -Bernoulli Polynomials

In this paper, we give some further properties of -adic --function of two variables, which is recently constructed by Kim (2005) and Cenkci (2006). One of the applications of these properties yields general classes of congruences for generalized -Bernoulli polynomials, which are -extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox (2000), Gunaratne (1995), and Young (1999, 2001).

[1]  Taekyun Kim,et al.  p-adic q-integrals associated with the Changhee–Barnes' q-Bernoulli polynomials , 2004 .

[2]  P. Young On the behavior of some two-variable p-adic L-functions , 2003 .

[3]  L. CARLITZ Arithmetic Properties of Generalized Bernoulli Numbers. , 1959 .

[4]  Neal Koblitz,et al.  On Carlitz's q-Bernoulli numbers , 1982 .

[5]  Taekyun Kim On p-adic q-L-functions and sums of powers , 2002, Discret. Math..

[6]  J. Diamond On the values of p-adic L-functions at positive integers , 1979 .

[7]  Taekyun Kim,et al.  A note on p-adic Carlitz's q-Bernoulli numbers , 2000, Bulletin of the Australian Mathematical Society.

[8]  R. Greenberg,et al.  On the behavior ofp-adicL-efunctions ats=0 , 1978 .

[9]  J. Diamond The $p$-adic log gamma function and $p$-adic Euler constants , 1977 .

[10]  L. Washington A note on p-adic L-functions , 1976 .

[11]  Taekyun Kim,et al.  ON EXPLICIT FORMULAS OF p-ADIC q-L-FUNCTIONS , 1994 .

[12]  H. Leopoldt Eine p-adische Theorie der Zetawerte. II. , 1975 .

[13]  G. Fox A method of Washington applied to the derivation of a two-variable p-adic L-function , 2003 .

[14]  N. Koblitz A new proof of certain formulas for $p$-adic $L$-functions , 1979 .

[16]  Leonard Carlitz,et al.  $q$-Bernoulli numbers and polynomials , 1948 .

[17]  H. S. Gunaratne A New Generalisation of the Kummer Congruence , 1995 .

[18]  Sums of powers of consecutive q-integers , 2005, math/0501531.

[19]  Y. Simsek,et al.  $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series , 2005, math/0502019.

[20]  L. Comtet,et al.  Advanced Combinatorics: The Art of Finite and Infinite Expansions , 1974 .