A Note on p-Adic Invariant Integral in the Rings of p-Adic Integers

TL;DR

This paper explores the properties of p-adic invariant q-integral at q=-1 within p-adic integers and demonstrates its applications to Euler numbers and polynomials.

Contribution

It introduces new properties of p-adic q-integral at q=-1 and applies them to study Euler numbers and polynomials.

Findings

Properties of p-adic q-integral at q=-1 are established.

Applications to Euler numbers and polynomials are demonstrated.

Potential for further study of p-adic integration properties.

Abstract

In [2], I constructed the p-adic q-integral on Zp. In this paper, we consider the properties of the p-adic invariant p-adic q-integral in the ring of p-adic integers at q=-1. Finally we give the some applications of p-adic q-integration at q=-1. These properties are useful and worthwhile to study Euler numbers and polynomials.