Hall (1947) proved that every real number is the sum of an
integer and two real numbers whose partial quotients are at most
.
Cusick (1971) proved that every real number is the sum of an
integer and two real numbers whose partial quotients are at least
. In a
recent paper, the authors proved that every real number is the sum of two real
numbers whose partial quotients diverge. In this paper, we prove an analogue of these
results for Laurent series.
Keywords
Diophantine approximation, continued fractions, function
field analogue, Hankel determinants, Hall's theorem,
Shulga's algorithm
