- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Mathematics
Volume 2013 (2013), Article ID 754134, 5 pages
http://dx.doi.org/10.1155/2013/754134
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.
Abstract
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.