Simultaneous multiplicative rational approximation to a real and a $p$-adic numbers

TL;DR

This paper provides new examples of pairs of real and p-adic numbers that satisfy a conjecture on simultaneous multiplicative approximation, advancing understanding in number theory.

Contribution

It introduces novel examples of real and p-adic number pairs that meet a specific conjecture on simultaneous multiplicative approximation.

Findings

New pairs of real and p-adic numbers satisfying the conjecture

Progress in understanding multiplicative approximation in number theory

Supports conjecture by providing explicit examples

Abstract

We give new examples of pairs composed of a real and a $p$-adic numbers that satisfy a conjecture on simultaneous multiplicative approximation by rational numbers formulated by Einsiedler and Kleinbock in 2007.