On a Brun-Titchmarsh inequality for multiplicative functions
On a multiplicative hybrid problem
On almost even arithmetical functions via orthonormal systems on Vilenkin groups
On consecutive integers divisible by the number of their divisors
We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
On fluctuations in the mean of a sum-of-divisors function
On fluctuations in the mean of a sum-of-divisors function, II
I give explicit values for the constant implied by an Omega-estimate due to Chen and Chen [CC] on the average of the sum of the divisors of n which are relatively coprime to any given integer a.
On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
On isolated, respectively consecutive large values of arithmetic functions
On rough and smooth neighbors.
We study the behavior of the arithmetic functions defined byF(n) = P+(n) / P-(n+1) and G(n) = P+(n+1) / P-(n) (n ≥ 1)where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.
On sets characterizing number-theoretical functions (II) (The set of "prime plus one"'s is a set of quasi-uniqueness)
On small eigenvalues of the Laplacian for ...(q). .
On some complex explicit formulae connected with the Mobius function. II
On some complex explicit formulae connected with the Mobius function. I
On some modifications of two theorems of Erdős
On sums of Ramanujan sums
On the asymptotic behavior of some counting functions
The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class group satisfies...
On the correlation of the truncated Liouville function
On the counting function for the generalized Niven numbers
Given an integer base and a completely -additive arithmetic function taking integer values, we deduce an asymptotic expression for the counting functionunder a mild restriction on the values of . When , the base sum of digits function, the integers counted by are the so-called base Niven numbers, and our result provides a generalization of the asymptotic known in that case.
On the determination of an additive arithmetical function by its local behaviour
On the difference of values of the kernel function at consecutive integers.