Diophantine approximation with partial sums of power series

Bruce C. Berndt, et al. "Diophantine approximation with partial sums of power series." Acta Arithmetica 161.3 (2013): 249-266. <http://eudml.org/doc/278990>.

@article{BruceC2013,
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.},
author = {Bruce C. Berndt, Sun Kim, M. Tip Phaovibul, Alexandru Zaharescu},
journal = {Acta Arithmetica},
keywords = {power series; continued fractions; partial sums; convergents},
language = {eng},
number = {3},
pages = {249-266},
title = {Diophantine approximation with partial sums of power series},
url = {http://eudml.org/doc/278990},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Bruce C. Berndt
AU - Sun Kim
AU - M. Tip Phaovibul
AU - Alexandru Zaharescu
TI - Diophantine approximation with partial sums of power series
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 3
SP - 249
EP - 266
AB - 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.
LA - eng
KW - power series; continued fractions; partial sums; convergents
UR - http://eudml.org/doc/278990
ER -