On a Two-Variable p-Adic lq-Function

Abstract EN

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.