Rafael Jakimczuk
División Matemática
Universidad Nacional de Luján
Buenos Aires
Argentina
Abstract:
We study some properties of functions that satisfy the condition
,
for
, i.e.,
.
We call these ``functions of slow increase'',
since they satisfy the condition
for all .
A typical example of a function of slow increase is the function
.
As an application, we obtain some general results on sequence of
positive integers that satisfy the asymptotic formula
, where is a function of slow increase.