# Hal\'{a}sz's theorem for Beurling generalized numbers

## TL;DR

This paper extends Halász's theorem to Beurling generalized numbers, demonstrating its validity under mild conditions related to the density of integers and bounds on primes.

## Contribution

It establishes the applicability of Halász's theorem to Beurling numbers with minimal assumptions on their distribution.

## Key findings

- Halász's theorem holds for Beurling numbers under mild hypotheses.
- Existence of positive density for generalized integers is sufficient.
- A Chebyshev upper bound for generalized primes is also sufficient.

## Abstract

We show that Hal\'{a}sz's theorem holds for Beurling numbers under the following two mild hypotheses on the generalized number system: existence of a positive density for the generalized integers and a Chebyshev upper bound for the generalized primes.