Andreas Weingartner

collaborators

5 papers

math.NT2026

Explicit bounds for Buchstab's function

Andreas Weingartner

Buchstab's function $I ¨ (u)$ describes the distribution of integers without small prime factors. We establish numerically explicit upper and lower bounds for $I ¨ (u)$ that are easy t…

math.NT2026

Explicit bounds for Dickman's function

Andreas Weingartner

Dickman's function $ρ (u)$ denotes the natural density of integers $n$ whose largest prime factor does not exceed $n^{1/ u}$ . We establish numerically explicit upper and lower bounds…

math.NT2026

A link between error terms when counting smooth and rough numbers

Andreas Weingartner

We establish a relationship between error terms appearing in estimates for the counting functions of smooth and rough numbers. We then apply this link to obtain an explicit upper b…

math.NT2026

Exceptions to the Erd\H os--Straus--Schinzel conjecture

Carl Pomerance, Andreas Weingartner

A famous conjecture of Erd\H os and Straus is that for every integer $n \geq 2$ , $4/ n$ can be represented as $1/ x + 1/ y + 1/ z$ , where $x, y, z$ are positive integers. This conjecture was ge…

math.NT2025

An extension of smooth numbers: multiple dense divisibility

Garo Sarajian, Andreas Weingartner

The $i$ -tuply $y$ -densely divisible numbers were introduced by a Polymath project, as a weaker condition on the moduli than $y$ -smoothness, in distribution estimates for primes in…