Counting multiplicative approximations

Sam Chow, Niclas Technau*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)241-250
Number of pages10
JournalRamanujan Journal
Issue number1
StatePublished - Sep 2023
Externally publishedYes


  • Counting
  • Littlewood conjecture
  • Metric diophantine approximation


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