On sums of degrees of the partial quotients in continued fraction expansions of Laurent series

AbstractFor any formal Laurent series x=∑n=v∞cnz−n with coefficients cn lying in some given finite field, let x=[a0(x);a1(x),a2(x),…] be its continued fraction expansion. It is known that, with respect to the Haar measure, almost surely, the sum of degrees of partial quotients dega1(x)+⋯+degan(x) grows linearly. In this note, we quantify the exceptional sets of points with faster growth orders than linear ones by their Hausdorff dimension, which covers an earlier result by J. Wu