On a problem of W. J. LeVeque concerning metric diophantine approximation
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Abstract:
We consider the diophantine approximation problem \[ \left \vert x-\frac {p}{q}\right \vert \leq \frac {f(\log q)}{q^2} \] where $f$ is a fixed function satisfying suitable assumptions. Suppose that $x$ is randomly chosen in the unit interval. In a series of papers that appeared in earlier issues of this journal, LeVeque raised the question of whether or not the central limit theorem holds for the solution set of the above inequality (compare also with some work of Erdős). Here, we are going to extend and solve LeVeque’s problem.References
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Additional Information
- Michael Fuchs
- Affiliation: Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8-10/113, 1040 Wien, Austria
- Address at time of publication: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan, R.O.C.
- Email: fuchs@stat.sinica.edu.tw
- Received by editor(s): February 7, 2002
- Received by editor(s) in revised form: September 18, 2002
- Published electronically: December 18, 2002
- Additional Notes: This work was supported by the Austrian Science Foundation FWF, grant S8302-MAT
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 1787-1801
- MSC (2000): Primary 11J83, 60F05
- DOI: https://doi.org/10.1090/S0002-9947-02-03225-7
- MathSciNet review: 1953525