Counting multiplicative approximations

A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals the same denominator, multiplying errors. In a lesser-known paper, Wang and Yu (Chin Ann Math 2:1–12, 1981) established an asymptotic formula for number such approximations, valid almost always. Using quantitative Koukoulopoulos–Maynard theorem Aistleitner–Borda–Hauke, together with bounds arising from theory Bohr sets, we deduce lower expected order magnitude inhomogeneous fibre refinements problem.