On Trace Sets of Restricted Continued Fraction Semigroups

Alex Kontorovich ()
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Alex Kontorovich: Rutgers University, Department of Mathematics

A chapter in Analysis at Large, 2022, pp 253-272 from Springer

Abstract: Abstract We record an argument due to Jean Bourgain which gives lower bounds on the size of the trace sets of certain semigroups related to continued fractions on finite alphabets. These bounds are motivated by the “Classical Arithmetic Chaos” Conjecture of McMullen (Dynamics of units and packing constants of ideals, 2012). Specifically, a power is gained in the asymptotic size of the trace set over a “trivial” exponent. The proof involves a new application of the Balog-Szemerédi-Gowers Lemma from additive combinatorics.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05331-3_11

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DOI: 10.1007/978-3-031-05331-3_11

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