English

Diophantine approximation by rational numbers of certain parity types

Number Theory 2024-03-20 v1

Abstract

For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd and odd/even rational numbers. We study algorithms to find best approximations by rational numbers of given parities and compare these algorithms with continued fraction expansions.

Keywords

Cite

@article{arxiv.2403.12341,
  title  = {Diophantine approximation by rational numbers of certain parity types},
  author = {Dong Han Kim and Seul Bee Lee and Lingmin Liao},
  journal= {arXiv preprint arXiv:2403.12341},
  year   = {2024}
}

Comments

22 pages, 6 figures