Diophantine approximation with arithmetic functions, I

TL;DR

This paper establishes a new theorem in Diophantine approximation, demonstrating how additive and multiplicative functions can be simultaneously approximated under specific regularity conditions on primes.

Contribution

It introduces a strong simultaneous Diophantine approximation theorem for additive and multiplicative functions with prime regularity assumptions.

Findings

Proves a strong simultaneous approximation theorem.

Shows approximation results depend on prime regularity.

Extends Diophantine approximation theory to new classes of functions.

Abstract

We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.