Partial quotients and representation of rational numbers

2012/08/16 by Jean Bourgain, Bourgain, Jean · 1 citation
Mathematics · #11A55 #11D68 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A55 #msc:11D68

paper · pdf · doi:10.48550/arxiv.1208.3402

arxiv created 2012/08/16 · arxiv updated 2012/08/17

Abstract

It is shown that there is an absolute constant C such that any rational \frac bq∈]0, 1[, (b, q)=1, admits a representation as a finite sum \frac bq=∑_α\frac b_αq_α where ∑_α∑_ia_i(\frac b_αq_α)<Clog q and \a_i(x)\ denotes the sequence of partial quotients of x.

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