English

Partial quotients and representation of rational numbers

Number Theory 2012-08-17 v1

Abstract

It is shown that there is an absolute constant CC such that any rational bq]0,1[,(b,q)=1\frac bq\in]0, 1[, (b, q)=1, admits a representation as a finite sum bq=αbαqα\frac bq=\sum_\alpha\frac {b_\alpha}{q_\alpha} where αiai(bαqα)<Clogq\sum_\alpha\sum_ia_i(\frac {b_\alpha}{q_\alpha})<C\log q and {ai(x)}\{a_i(x)\} denotes the sequence of partial quotients of xx.

Keywords

Cite

@article{arxiv.1208.3402,
  title  = {Partial quotients and representation of rational numbers},
  author = {Jean Bourgain},
  journal= {arXiv preprint arXiv:1208.3402},
  year   = {2012}
}
R2 v1 2026-06-21T21:51:34.409Z