Diophantine approximation by rational numbers of certain parity types

Dong Han Kim, Seul Bee Lee, Lingmin Liao

Published 2024-03-19Version 1

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.