English

Tong's spectrum for Rosen continued fractions

Number Theory 2007-08-27 v1

Abstract

The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best possible upper bound for the minimum in appropriate consecutive blocks of approximation coefficients (in the sense of Diophantine approximation by continued fraction convergents). We also obtain metrical results for large blocks of ``bad'' approximations.

Keywords

Cite

@article{arxiv.0708.3257,
  title  = {Tong's spectrum for Rosen continued fractions},
  author = {Cor Kraaikamp and Thomas A. Schmidt and Ionica Smeets},
  journal= {arXiv preprint arXiv:0708.3257},
  year   = {2007}
}

Comments

22 pages, 5 figures

R2 v1 2026-06-21T09:10:11.787Z