The aim of the project is to further develop methods used in the algebraic, combinatorial and analytic number theoery and thus to contribute to a better understanding of some important aspects of the arithmetical structure of the sets of integers, rational and algebraic numbers, and their underlying structures, and to extend some of these relations to arithmetical objects build on some more abstract premises as arithmetical semigroups or divisorial structure of ordered groups. Subject of study will be various density relations of number sets, questions connected with irrationality and transcendency criteria of numbers, then the theory of uniform distribution of sequences of real numbers, and properties of arithmetic structures of sets of arithmetical functions, or their generalizations in terms of abstract arithmetical semigroups. Methods will be developed which are used for characterizations of fundamental aspects of algebraic number fields and their extensions and those describing properties of their ideal structure, or those used to study abstract ideal theory in various algebraic systems and in the theory of divisors of ordered groups.

Publications