Fourier Dimension Estimates for Sets of Exact Approximation Order: The Well-Approximable Case

Robert Fraser, Reuben Wheeler

Type: Article

Publication Date: 2022-10-07

Citations: 5

DOI: https://doi.org/10.1093/imrn/rnac256

Abstract

Abstract We obtain a Fourier dimension estimate for sets of exact approximation order introduced by Bugeaud for certain approximation functions $\psi $. This Fourier dimension estimate implies that these sets of exact approximation order contain normal numbers.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (22)

Action	Title	Year	Authors
+ PDF Chat	On the theorem of Jarník and Besicovitch	1981	Robert Kaufman
+	Analyse de Fourier des fractions continues a quotients restreints	2003	Martine Queffélec
+ PDF Chat	On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets	1998	Christian Bluhm
+	Sets of exact approximation order by rational numbers	2003	Yann Bugeaud
+	Über die metrische Theorie der diophantischen Approximation	1958	P. Szüsz
+	Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers	1934	A. S. Besicovitch
+ PDF Chat	On singular monotonic functions whose spectrum has a given Hausdorff dimension	1951	R. Salem
+ PDF Chat	On Weyl's criterion for uniform distribution.	1963	H. Davenport P. Erdős W. J. LeVeque
+	Continued fractions and Fourier transforms	1980	Robert Kaufman
+	Einige S�tze �ber Kettenbr�che, mit Anwendungen auf die Theorie der Diophantischen Approximationen	1924	A. Khintchine