characterization of additive functions, pi-regular sequence of measures, limit-periodic arithmetical functions, Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions, Multiplicative number theory, arithmetical functions, Harmonic analysis on specific compact groups, Metric theory of other algorithms and expansions; measure and Hausdorff dimension, compactification of the set of integers, uniformly almost periodic functions, limit-distribution of, product-measure, multiplicative functions, almost periodic number-theoretical functions, Gelfand's theory