## Abstract

Assume \(z\in \mathfrak F:=\{x+iy: x,y\in[-1/2,1/2)\}\) has its Hurwitz continued fraction expansion \([0;a_1(z),a_2(z),\dots]\) where \(a_j(z)\) are Gaussian integers and \(|a_j(z)|\ge \sqrt 2\). For any \(n\ge 1\), write \(S_n(z)=\sum_{j=1}^{n}a_j(z)\) and \(R_n(z)=\sum_{j=1}^{n}|a_j(z)|\) . It is known that for \(\mathcal L^2\)-almost every \(z\) , \(S_n(z)/n\) and \(R_n(z)/n\) converge to the constants \(W\) and \(C\) respectively, where \(\mathcal L^2\) denotes the 2-dimensional Lebesgue measure. We show that the sets

and

have full Hausdorff dimensions, where \(w_1, w_2\in \mathbb{C}\) and \(0<C\le \alpha_1\le \alpha_2<\infty \).

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## Acknowledgement

We thank the referee for careful reading of the paper and helpful comments and corrections which improved the paper substantially.

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He, Y., Xiao, Q. On sums of partial quotients in Hurwitz continued fraction expansions.
*Acta Math. Hungar.* **170**, 17–32 (2023). https://doi.org/10.1007/s10474-023-01345-3

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DOI: https://doi.org/10.1007/s10474-023-01345-3