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

On a Two-Variable p-Adic lq-Function

Min-Soo Kim,1 Taekyun Kim,2 D. K. Park,3 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

Received 18 December 2007; Accepted 28 May 2008

Academic Editor: Allan Peterson

Copyright © 2008 Min-Soo Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.