Biró, András and Deshouillers, JM. and T. Sós, Vera (2001) Good approximation and characterization of subgroups of R/Z. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 38 (14). pp. 97113. ISSN 00816906

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Abstract
Let α be a real irrational number and A = (x n) be a sequence of positive integers. We call A a characterizing sequence of α or of the group ℤα mod 1 if lim ∥nβ∥ = 0 n∈A n→∞ if and only if β ∈ ℤα mod 1. In the present paper we prove the existence of such characterizing sequences, also for more general subgroups of ℝ/ℤ. In the special case ℤα mod 1 we give explicit construction of a characterizing sequence in terms of the continued fraction expansion of α. Further, we also prove some results concerning the growth and gap properties of such sequences. Finally, we formulate some open problems.
Item Type:  Article 

Uncontrolled Keywords:  continued fractions; Distribution mod 1; Characterizing sequences; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  27 Jun 2020 07:10 
Last Modified:  27 Jun 2020 07:10 
URI:  http://real.mtak.hu/id/eprint/110616 
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