This project is concerning the theory of arithmetical functions, which is a classical but active part of number
theory.
Its main objectives are the following:
1. To investigate certain special arithmetical functions of one variable and to deduce for them asymptotic
formulae with sharp error terms. To improve certain existing error terms, especially for functions involving
exponential divisors and regular integers (mod n). To obtain unconditional results, as well as results assuming
the Riemann hypothesis.
2. To study certain special arithmetical functions of several variables in connection with enumerative problems
in number theory and combinatorics, considered in recent papers by other authors.
3. To investigate the problem of giving exact and approximate formulae for the number solutions of quadratic
and higher degree congruences and for the number of subgroups of finite Abelian groups.
The applicant intends to continue his research work and his collaboration with Professor Werner Georg Nowak,
begun at the Institute of Mathematics, Universität für Bodenkultur Vienna, under the project Nr. P20847-N18 of
the Austrian Science Fund (FWF), to be closed on 31. January 2012.