Multiplikative Funktionen auf kurzen Intervallen.
Multiplikative Funktionen mehrerer Variablen.
Natural divisors and the brownian motion
A model of the Brownian motion defined in terms of the natural divisors is proposed and weak convergence of the related measures in the space [0,1] is proved. An analogon of the Erdös arcsine law, known for the prime divisors [6] (see [14] for the proof), is obtained. These results together with the author’s investigation [15] extend the systematic study [9] of the distribution of natural divisors. Our approach is based upon the functional limit theorems of probability theory.
New Omega Theorems for Two Classical Lattice Points Problems.
Non-divisibility of some multiplicative functions
Normal numbers and the middle prime factor of an integer
Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.
Normal order for a function associated with factorization into irreducibles
Normal orders for certain functions associated with factorizations in number fields
Notes on the method of Frobenian functions with applications to Fourier coefficients of modular forms
Number of solutions of certain congruences
Numbers with large prime factors
Odd values of the Ramanujan -function
On a certain additive function on the Gaussian integers
On a certain class of arithmetic functions
A homothetic arithmetic function of ratio is a function such that for every . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of in terms of the period and the ratio of .
On a class of arithmetic convolutions involving arbitrary sets of integers.
On a class of arithmetical functions connected with multiplicative functions.
On a conjecture of Narkiewicz about functions with non-decreasing normal order
On a divisor problem related to the Epstein zeta-function, IV
On a generalization of a formula of Sierpiński.
On a generalization of a formula of Sierpiński. II.