Statistically characterized subgroups of the circle

In this paper, we introduce a new version of characterized subgroups of the circle group T that we call statistically characterized subgroups (briefly, s-characterized subgroups). We primarily investigate these subgroups for arithmetic sequences of integers and show that these subgroups are essentially different and strictly larger in size than the much investigated class of characterized subgroups, having cardinality c but remaining nontrivial (i.e. different from T) though remaining topologically nice.