On A two-variable p-adic l_q function

TL;DR

This paper explores a two-variable p-adic l_q-function, demonstrating its series expansion that interpolates generalized q-Euler polynomial combinations at non-positive integers, building on classical methods.

Contribution

It provides a new construction of the two-variable p-adic l_q-function using Washington's approach, extending classical interpolation techniques.

Findings

The p-adic l_q-function admits a series expansion interpolating generalized q-Euler polynomials.

The construction generalizes previous single-variable p-adic L-functions.

The method offers a novel proof based on classical p-adic analysis techniques.

Abstract

We prove that a two-variable p-adic l_q-function has the series p-adic expansion which interpolates a linear combinations of terms of the generalized q-Euler polynomials at non positive integers. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given this note is due to Washington