29 citations · 32 across the 8 of their papers we have counts for
19 papers
Uniform distribution of modulo one for a family of integer sequences
Andreas Weingartner
We show that the sequence is uniformly distributed modulo 1, for every irrational , provided belongs to a certain family of integer seque…
An Erdős-Kac theorem for integers with dense divisors
Gérald Tenenbaum, Andreas Weingartner
We show that for large integers , whose ratios of consecutive divisors are bounded above by an arbitrary constant, the number of prime factors follows an approximate normal dist…
Somewhat smooth numbers in short intervals
Andreas Weingartner
We use exponent pairs to establish the existence of many -smooth numbers in short intervals , when . In particular, is admissible. Assuming…
The mean number of divisors for rough, dense and practical numbers
Andreas Weingartner
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 number…
The number of prime factors of integers with dense divisors
Andreas Weingartner
We show that for integers , whose ratios of consecutive divisors are bounded above by an arbitrary constant, the normal order of the number of prime factors is ,…
An extension of the Siegel-Walfisz theorem
Andreas Weingartner
We extend the Siegel-Walfisz theorem to a family of integer sequences that are characterized by constraints on the size of the prime factors. Besides prime powers, this family incl…