Biró, András and T. Sós, Vera (2003) Strong Characterizing Sequences in Simultaneous Diophantine Approximation. JOURNAL OF NUMBER THEORY, 99 (2). pp. 405414. ISSN 0022314X

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Abstract
Answering a question of Liardet. we prove that if 1, alpha(1), alpha(2)...... alpha(t) are real numbers linearly independent over the rationals, then there is an infinite subset A of the positive integers such that for real beta, we have (  denotes the distance to the nearest integer) Sigma(nequivalent toA)nbeta<infinity if and only if beta is a linear combination with integer coefficients of 1, alpha(1), alpha(2,)..., alpha(t). The proof combines elementary ideas with a deep theorem of Freiman on set addition. Using Freiman's theorem, we prove a lemma on the structure of Bohr sets, which may have independent interest. (C) 2002 Elsevier Science (USA). All rights reserved.
Item Type:  Article 

Uncontrolled Keywords:  Freiman's theorem; Characterizing sequences; Bohr sets; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA71 Number theory / számelmélet 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  29 Jun 2020 08:17 
Last Modified:  29 Jun 2020 08:17 
URI:  http://real.mtak.hu/id/eprint/110617 
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