Bogmér, A.; Horváth, M.; Sörvegjártó, A. On some problems of I. Joó. (English) Zbl 0766.11004 Acta Math. Hung. 58, No. 1-2, 153-155 (1991). The authors provide negative answers to two problems raised bo I. Joó: Does there exist an expansion \(1=\sum_{i=1}^ \infty q^{-n_ i}\) satisfying \(\sup(n_{i+1}-n_ i)=\infty\) for every \(1<q<(1+\sqrt{5})/2\) and, for every \(1<q<2\) is the existence of such an expansion equivalent to the existence of \(2^{\aleph_ 0}\) such different expansions? Reviewer: A.Knopfmacher (Wits) Cited in 6 Documents MSC: 11A67 Other number representations Keywords:Pisot numbers; expansions PDF BibTeX XML Cite \textit{A. Bogmér} et al., Acta Math. Hung. 58, No. 1--2, 153--155 (1991; Zbl 0766.11004) Full Text: DOI References: [1] J. W. S. Cassels,An Introduction to Diophantine Approximation, Cambridge University Press, 1957. · Zbl 0077.04801 [2] I. N. Stewart and D. O. Tall,Algebraic Number Theory, Chapman and Hall (London, 1979). · Zbl 0413.12001 [3] I. Joó, On Riesz bases,Annales Univ. Sci. Budapest., Sectio Math.,31 (1988), 141–153. · Zbl 0674.46006 [4] P. Erdos and I. Joó, On the expansion \(1 = \sum {q^{ - n_i } } \) ,Per. Math. Hung.,23 (1991). [5] P. Erdos, M. Joó and I. Joó, On a problem of Tamás Varga (to appear). [6] J. Dufresnoy, C. Pisot, Sur un ensemble fermé d’entiers algébriques,Ann. Sci. Éc. Norm. Sup. Paris,70 (1953), 105–134. · Zbl 0051.02904 [7] I. Joó and M. Joó, On an arithmetical property of ,Publ. Math. Debrecen,37 (1990). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.