I. D. Kan, D. A. Frolenkov, “A strengthening of a theorem of Bourgain and Kontorovich”, Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 2,Pages <nobr>87

This article is cited in 16 papers

A strengthening of a theorem of Bourgain and Kontorovich

I. D. Kan^a, D. A. Frolenkov^b

^a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: We prove that the set of positive integers contains a positive proportion of numbers satisfying Zaremba's conjecture with $A=7$. This result strengthens a similar theorem of Bourgain and Kontorovich obtained for $A=50$.

Keywords: continued fraction, continuant, exponential sums.

UDC: 511.321+511.31

MSC: 11A55, 11B05, 11P55

Received: 10.07.2012
Revised: 24.05.2013

DOI: 10.4213/im8032