Abstract and Applied Analysis
Volume 2008 (2008), Article ID 360517, 10 pages
doi:10.1155/2008/360517

On a Two-Variable p-Adic lq-Function

Min-Soo Kim1 , Taekyun Kim2 , D.K. Park3 and Jin-Woo Son1

1Department of Mathematics, Kyungnam University, Masan 631701, South Korea
 2Division of General Education-Mathematics, Kwangwoon University, Seoul 139701, South Korea
 3Department of Physics, Kyungnam University, Masan 631701, South Korea

Abstract

We prove that a two-variable p-adic lq-function has the series expansion lp,q(s,t,χ)=([2]q/[2]F)∑a=1,(p,a)=1F(−1)a(χ(a)qa/〈a+pt〉s)∑m=0∞(−sm)(F/〈a+pt〉)mEm,qF* which interpolates the values lp,q(−n,t,χ)=En,χn,q∗(pt)−pnχn(p)([2]q/[2]qp)En,χn,qp∗(t), whenever n is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this note is due to Washington.