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Summary
Assume z ? := {x + iy : x, y E [-1/2, 1/2)} has its Hurwitz continued fraction expansion [0; a1(z), a2(z), ... ] where aj(z) are Gaussian integers and |aj(z)| > V/2. For any n > 1, write Sn(z) = Snj=1 aj(z) and Rn(z) = Snj =1 |aj(z)|. It is known that for L2-almost every z, Sn(z)/n and Rn(z)/n con- verge to the constants W and C respectively, where L2 denotes the 2-dimensional Lebesgue measure. We show that the sets {E(w1, w2) := z E : the accumulation points of and ( S-n(z)1 } n'1 are w1 and w2 n {R-n(z) R-n(z) } F(a1, a2) := z E : liminf n = a1 and lim sup n = a2 n-).oo n-).oo have full Hausdorff dimensions, where w(1), w(2) E C and 0 < C < a1 < a2 < oo.
