Counting multiplicative approximations Article Swipe
Related Concepts
Mathematics
Rational number
Multiplicative function
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Sam Chow
,
Niclas Technau
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2203.10380
· OA: W4323366747
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2203.10380
· OA: W4323366747
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 (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.
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