2008/06/09 by Kraaikamp, Cor, Smeets, Ionica
#11K50 #28D05 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.0806.1457
In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next approximation. We sharpen his results with a geometric method and give both sharp upper and lower bounds. We also calculate the asymptotic frequency that these bounds occur.