For any irrational number define the Lagrange constant by
The set of all values taken by as varies is called the Lagrange spectrum . An irrational is called attainable if the inequality
holds for infinitely many integers and . We call a real number admissible if there exists an irrational attainable such that . In a previous paper we constructed an example of a nonadmissible element in the Lagrange spectrum. In the present paper we give a necessary and sufficient condition for admissibility of a Lagrange spectrum element. We also give an example of an infinite sequence of left endpoints of gaps in which are not admissible.
"Admissible endpoints of gaps in the Lagrange spectrum." Mosc. J. Comb. Number Theory 8 (1) 47 - 56, 2019. https://doi.org/10.2140/moscow.2019.8.47