Imre Kátai

On a problem of P. Erdös

Abstract We prove the following conjecture of Erdos. If f(n) is an additive function and 1 x Σ n≤x |f(n + 1) − f(n)| tends to zero as x tends to infinity, then f(n) is a constant multiple of log n.

Investigations in the theory of q-additive and q-multiplicative functions. II

The mean values of g1(a1n)...gk(akn) are investigated where g1...gk are q-multiplicative functions the absolute values of which are 1. Some applications are given.

ON A PROBLEM ON NORMAL NUMBERS RAISED BY IGOR SHPARLINSKI

Given an integer

A renewal theorem for random walks in multidimensional time

d\ge 2

The Characterization of nir as a Multiplicative Function

, a

Construction of normal numbers using the distribution of the \(kth\) largest prime factor

d

A Comparative Result for Multiplicative Functions

-{\it normal number}, or simply a {\it normal number}, is an irrational number whose

On the pairs of multiplicative functions satisfying some relations

d

Continuous additive functions and difference equations of infinite order

-ary expansion is such that any preassigned sequence, of length

The Number of Prime Factors Function on Shifted Primes and Normal Numbers

k\ge 1