Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion

摘要

This paper investigates the quadratic irrationals that arise as periodic points of the Gauss type shift associated to the odd continued fraction expansion. It is shown that these numbers, which we call O-reduced, when ordered by the length of the associated closed primitive geodesic on some modular surface GammaH, are equidistributed with respect to the Lebesgue absolutely continuous invariant probability measure of the Odd Gauss shift. (c) 2022 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.