|
Session 1. Analytic Number Theory
|
Oscillations of arithmetical functions defined by factorization-related properties |
Maciej Radziejewski, Adam Mickiewicz University, Poland
|
|
|
We show some results on oscillations of the counting functions of
subsets of arithmetical semigroups defined by factorial
properties. The main problem in showing the existence of
oscillations is to show the existence of an appropriate singularity
of the related zeta function. To do that, one needs to know at least
the general shape of the zeta function. However, there are important
examples of semigroup subsets (outside of the class of sets called
\(\Omega\) sets by the author), for which this may be a difficult
task. We will show some general results related to \(\Omega\) sets
and attempt to tackle some subsets outside of this class.
|
|
| Print version |
|
