The Digamma function, Euler-Lehmer constants and their $p$-adic counterparts

TL;DR

This paper extends known results on the digamma function at rational points and explores the properties of p-adic Euler-Lehmer constants, contributing to number theory and special functions.

Contribution

It generalizes previous findings by Murty and Saradha on the digamma function and p-adic Euler-Lehmer constants, broadening their applicability.

Findings

Extended the digamma function results to broader rational arguments.

Analyzed the nature of p-adic Euler-Lehmer constants in new contexts.

Provided new insights into p-adic special functions and their properties.

Abstract

The goal of this article is twofold. We first extend a result of Murty and Saradha \cite{MS} related to the digamma function at rational arguments. Further, we extend another result of the same authors \cite{MS1} about the nature of $p$-adic Euler-Lehmer constants.