Statistically characterized subgroups of the circle (II): Continued fractions

In this note, we continue the investigation of new version characterized subgroups circle group T, namely, “statistically subgroups” (shortly, “s-characterized subgroups”) recently introduced in [12]. We primarily investigate these for sequences arising out continued fraction representation irrational numbers α line [22] and [20] (followed by [3], [4], [5]) comparing their main results notion show that Borel are strictly larger size (so nontrivial) than corresponding subgroups, always having cardinality c containing subgroup 〈α〉 process answer Open Question 6.4 [12] which had asked about s-characterized celebrated Fibonacci sequence.