Good approximation and characterization of subgroups of R = Z

A. Bíró; J. M. Deshouillers; Vera T. Sós

doi:10.1556/sscmath.38.2001.1-4.7

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 38: Issue 1-4

Good approximation and characterization of subgroups of R = Z

Authors:

A. Bíró

A. Bíró Please ask the editor of the journal.

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J. M. Deshouillers

J. M. Deshouillers Please ask the editor of the journal.

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Vera T. Sós

Vera T. Sós Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences Reáltanoda u. 13-15. 1053 Budapest

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Pages:: 97–113

Online Publication Date:: 22 Jul 2005

Publication Date:: 01 May 2001

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.38.2001.1-4.7

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Let be a real irrational number and A =(xn) be a sequence of positive integers. We call A a characterizing sequence of or of the group Z mod 1 if lim n 2A n !1 k k =0 if and only if 2 Z mod 1. In the present paper we prove the existence of such characterizing sequences, also for more general subgroups of R = Z . Inthespecialcase Z mod 1 we give explicit construction of a characterizing sequence in terms of the continued fraction expansion of. Further, we also prove some results concerning the growth and gap properties of such sequences. Finally, we formulate some open problems.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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