Andreas Weingartner
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Andreas Weingartner has a total of 10 co-authors. Here are the top co-authors by number of shared publications:
- Carl Pomerance
Department of Mathematics, Dartmouth College, Hanover, USA
3 shared publications - Carl Pomerance
Dartmouth College
2 shared publications - Igor E. Shparlinski
School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
2 shared publications - Lola Thompson
Department of MathematicsOberlin CollegeOberlinOH44074U.S.A.
2 shared publications - Roger C. Baker
Department of Mathematics, Brigham Young University, Provo, USA
2 shared publications - Eric Saias
Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation (LPSM) 4, place Jussieu, 75252 Paris Cedex 05, France
1 shared publication
Latest Publications
- 14 January 2026
- Published by Springer Nature in The Ramanujan Journal
- Vol. 69 (2) , 31
Exceptions to the Erdős–Straus–Schinzel conjecture
- 14 January 2026
- Published by Springer Nature in The Ramanujan Journal
- Vol. 69 (2) , 31
Exceptions to the Erdős–Straus–Schinzel conjecture
- 17 June 2025
- Published by Springer Nature in Research in Number Theory
- Vol. 11 (3) , 1-32
The Schinzel-Szekeres function
- 17 June 2025
- Published by Springer Nature in Research in Number Theory
- Vol. 11 (3) , 1-32
The Schinzel-Szekeres function
- Open Access
- 1 December 2023
- Published by Walter de Gruyter GmbH in Uniform distribution theory
- Vol. 18 (2) , 19-30
Uniform Distribution of αn Modulo One for A family of Integer Sequences
We show that the sequence (αn) n ∈ℬ is uniformly distributed modulo 1, for every irrational α, provided ℬ belongs to a certain family of integer sequences, which includes the prime, almost prime, squarefree, practical, densely divisible and lexicographical numbers. We also give an estimate for the discrepancy if α has finite irrationality measure.
- 1 December 2023
- Published by Walter de Gruyter GmbH in Uniform distribution theory
- Vol. 18 (2) , 19-30
Open AccessUniform Distribution of αn Modulo One for A family of Integer Sequences
We show that the sequence (αn) n ∈ℬ is uniformly distributed modulo 1, for every irrational α, provided ℬ belongs to a certain family of integer sequences, which includes the prime, almost prime, squarefree, practical, densely divisible and lexicographical numbers. We also give an estimate for the discrepancy if α has finite irrationality measure.
- Open AccessUniform distribution of $αn$ modulo one for a family of integer sequencesWe show that the sequence $(αn)_{n\in \mathcal{B}}$ is uniformly distributed modulo 1, for every irrational $α$, provided $\mathcal{B}$ belongs to a certain family of integer sequences, which includes the prime, almost prime, squarefree, practical, densely divisible and lexicographical numbers. We also give an estimate for the discrepancy if $α$ has finite irrationality measure.Open AccessUniform distribution of $αn$ modulo one for a family of integer sequencesWe show that the sequence $(αn)_{n\in \mathcal{B}}$ is uniformly distributed modulo 1, for every irrational $α$, provided $\mathcal{B}$ belongs to a certain family of integer sequences, which includes the prime, almost prime, squarefree, practical, densely divisible and lexicographical numbers. We also give an estimate for the discrepancy if $α$ has finite irrationality measure.
- Open Access
- 30 June 2023
- Published by World Scientific Pub Co Pte Ltd in International Journal of Number Theory
- Vol. 19 (10) , 2333-2351
The mean number of divisors for rough, dense and practical numbers
We give asymptotic estimates for the mean number of divisors of integers without small prime factors, integers with bounded ratios of consecutive divisors, and for practical numbers. In the last case, this confirms a conjecture of Margenstern.
- 30 June 2023
- Published by World Scientific Pub Co Pte Ltd in International Journal of Number Theory
- Vol. 19 (10) , 2333-2351
Open AccessThe mean number of divisors for rough, dense and practical numbers
We give asymptotic estimates for the mean number of divisors of integers without small prime factors, integers with bounded ratios of consecutive divisors, and for practical numbers. In the last case, this confirms a conjecture of Margenstern.
- Open Access
The mean number of divisors for rough, dense and practical numbers
We give asymptotic estimates for the mean number of divisors of integers without small prime factors, integers with bounded ratios of consecutive divisors, and for practical numbers. In the last case, this confirms a conjecture of Margenstern.
Open AccessThe mean number of divisors for rough, dense and practical numbers
We give asymptotic estimates for the mean number of divisors of integers without small prime factors, integers with bounded ratios of consecutive divisors, and for practical numbers. In the last case, this confirms a conjecture of Margenstern.
- 16 April 2022
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mathematics
- Vol. 75 (1) , 161-195
An Erdős–Kac theorem for integers with dense divisors
We show that for large integers n, whose ratios of consecutive divisors are bound above by an arbitrary constant, the number of prime factors follows an approximate normal distribution, with mean $C \log_2 n$ and variance $V \log_2 n$, where $C=1/(1-{\rm e}^{-\gamma})\approx 2.280$ and V ≈ 0.414. This result is then generalized in two different directions.- 16 April 2022
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mathematics
- Vol. 75 (1) , 161-195
An Erdős–Kac theorem for integers with dense divisors
We show that for large integers n, whose ratios of consecutive divisors are bound above by an arbitrary constant, the number of prime factors follows an approximate normal distribution, with mean $C \log_2 n$ and variance $V \log_2 n$, where $C=1/(1-{\rm e}^{-\gamma})\approx 2.280$ and V ≈ 0.414. This result is then generalized in two different directions.- 22 February 2022
- Published by Springer Nature in The Ramanujan Journal
- Vol. 60 (2) , 447-453
Somewhat smooth numbers in short intervals
- 22 February 2022
- Published by Springer Nature in The Ramanujan Journal
- Vol. 60 (2) , 447-453
Somewhat smooth numbers in short intervals
- Open Access
The number of prime factors of integers with dense divisors
We show that for integers $n$, whose ratios of consecutive divisors are bounded above by an arbitrary constant, the normal order of the number of prime factors is $C \log \log n$, where $C=(1-e^{-\gamma})^{-1} = 2.280...$ and $\gamma$ is Euler's constant. We explore several applications and resolve a conjecture of Margenstern about practical numbers.Open AccessThe number of prime factors of integers with dense divisors
We show that for integers $n$, whose ratios of consecutive divisors are bounded above by an arbitrary constant, the normal order of the number of prime factors is $C \log \log n$, where $C=(1-e^{-\gamma})^{-1} = 2.280...$ and $\gamma$ is Euler's constant. We explore several applications and resolve a conjecture of Margenstern about practical numbers. - Open Access
Somewhat smooth numbers in short intervals
We use exponent pairs to establish the existence of many $x^a$-smooth numbers in short intervals $[x-x^b,x]$, when $a>1/2$. In particular, $b=1-a-a(1-a)^3$ is admissible. Assuming the exponent-pairs conjecture, one can take $b=(1-a)/2+\epsilon$. As an application, we show that $[x-x^{0.4872},x]$ contains many practical numbers when $x$ is large.Open AccessSomewhat smooth numbers in short intervals
We use exponent pairs to establish the existence of many $x^a$-smooth numbers in short intervals $[x-x^b,x]$, when $a>1/2$. In particular, $b=1-a-a(1-a)^3$ is admissible. Assuming the exponent-pairs conjecture, one can take $b=(1-a)/2+\epsilon$. As an application, we show that $[x-x^{0.4872},x]$ contains many practical numbers when $x$ is large.