Diophantine approximation with partial sums of power series
Volume 161 / 2013
Acta Arithmetica 161 (2013), 249-266
MSC: Primary 11J68; Secondary 11J17, 11J70.
DOI: 10.4064/aa161-3-4
Abstract
We study the question: How often do partial sums of power series of functions coalesce with convergents of the (simple) continued fractions of the functions? Our theorems quantitatively demonstrate that the answer is: not very often. We conjecture that in most cases there are only a finite number of partial sums coinciding with convergents. In many of these cases, we offer exact numbers in our conjectures.
