Published September 8, 2022
| public
Journal Article
Counting multiplicative approximations
- Creators
- Chow, Sam
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Technau, Niclas
Chicago
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Abstract
A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals of the same denominator, multiplying the errors. In a lesser-known paper, Wang and Yu (Chin Ann Math 2:1–12, 1981) established an asymptotic formula for the number of such approximations, valid almost always. Using the quantitative Koukoulopoulos–Maynard theorem of Aistleitner–Borda–Hauke, together with bounds arising from the theory of Bohr sets, we deduce lower bounds of the expected order of magnitude for inhomogeneous and fibre refinements of the problem.
Additional Information
We thank Jakub Konieczny for raising the question, as well as for feedback on an earlier version of this manuscript, and we thank Christoph Aistleitner for a helpful conversation. NT was supported by a Schrödinger Fellowship of the Austrian Science Fund (FWF): Project J 4464-N.Additional details
- Eprint ID
- 116693
- Resolver ID
- CaltechAUTHORS:20220908-223703957
- Fonds Zur Förderung der Wissenschaftlichen Forschung (FWF)
- J 4464-N
- Created
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2022-09-08Created from EPrint's datestamp field
- Updated
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2022-09-08Created from EPrint's last_modified field