On p-adic q-l-functions and sums of powers

Abstract In this paper, we give an explicit p -adic expansion of ∑ j = 1 ( j , p ) = 1 n p ( − 1 ) j q j [ j ] q r as a power series in n . The coefficients are values of p -adic q - l -function for q -Euler numbers.

[1]  Taekyun Kim Multiple p-adic L-function , 2005, math/0505133.

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

[3]  M. Mansour,et al.  A Note on q−Bernoulli Numbers and Polynomials , 2006 .

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

[5]  Ravi P. Agarwal,et al.  Exploring the multiple Changhee q-Bernoulli polynomials , 2005, Int. J. Comput. Math..

[6]  Taekyun Kim,et al.  On aq-Analogue of thep-Adic Log Gamma Functions and Related Integrals , 1999 .

[7]  Ravi P. Agarwal,et al.  A numerical investigation of the roots of q-polynomials , 2006, Int. J. Comput. Math..

[8]  Taekyun Kim q-Euler numbers and polynomials associated with p-adic q-integrals , 2007 .

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

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

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

[12]  Taekyun Kim,et al.  On the q-extension of Euler and Genocchi numbers , 2007 .

[13]  T. Kim A note on q-Volkenborn integration , 2005 .

[14]  Boris A Kupershmidt Reflection Symmetries of q-Bernoulli Polynomials , 2005 .

[15]  L. Washington Introduction to Cyclotomic Fields , 1982 .

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

[17]  Lawrence C. Washington,et al.  p-AdicL-Functions and Sums of Powers , 1998 .