Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Equipartition of interval partitions and an application to number theory


Authors: Karma Dajani and Adam Fieldsteel
Journal: Proc. Amer. Math. Soc. 129 (2001), 3453-3460
MSC (1991): Primary 11Kxx, 28Dxx
Published electronically: June 27, 2001
MathSciNet review: 1860476
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We give wider application and simpler proofs of results describing the rate at which the digits of one number-theoretic expansion determine those of another. The proofs are based on general measure-theoretic covering arguments and not on the dynamics of specific maps.


References [Enhancements On Off] (What's this?)

  • [BBDK] Jose Barrionuevo, Robert M. Burton, Karma Dajani, and Cor Kraaikamp, Ergodic properties of generalized Lüroth series, Acta Arith. 74 (1996), no. 4, 311–327. MR 1378226
  • [BDK] Bosma, W., K. Dajani and C. Kraaikamp - Entropy and counting correct digits, University of Nijmegen, report no. 9925, 1999. http://www-math.sci.kun.nl /math/onderzoek/reports/reports1999.html
  • [B] Patrick Billingsley, Ergodic theory and information, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0192027
  • [L] Gustav Lochs, Vergleich der Genauigkeit von Dezimalbruch und Kettenbruch, Abh. Math. Sem. Univ. Hamburg 27 (1964), 142–144 (German). MR 0162753
  • [R] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar 8 (1957), 477–493. MR 0097374
  • [S] Fritz Schweiger, Ergodic theory of fibred systems and metric number theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. MR 1419320

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11Kxx, 28Dxx

Retrieve articles in all journals with MSC (1991): 11Kxx, 28Dxx


Additional Information

Karma Dajani
Affiliation: Department of Mathematics, Utrecht University, 3508TA Utrecht, The Netherlands
Email: dajani@math.uu.nl

Adam Fieldsteel
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: afieldsteel@wesleyan.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06299-2
Keywords: Entropy, ergodic, continued fraction, number-theoretic fibered map
Received by editor(s): March 8, 2000
Published electronically: June 27, 2001
Additional Notes: The first author was partially supported by NWO grant no. 61-449
We wish to thank Ethan Coven for useful observations.
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society