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Journal of Mathematics
Volume 2013 (2013), Article ID 754134, 5 pages
Research Article

Dimension Estimates for Certain Sets of Infinite Complex Continued Fractions

Institut für Mathematik, Technical University Clausthal, Reitstallweg 9, 38640 Goslar, Germany

Received 13 August 2012; Accepted 2 October 2012

Academic Editor: Stefan Siegmund

Copyright © 2013 J. Neunhäuserer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove upper and lower estimates on the Hausdorff dimension of sets of infinite complex continued fractions with finitely many prescribed Gaussian integers. Particulary we will conclude that the dimension of theses sets is not zero or two and there are such sets with dimension greater than one and smaller than one.