论文标题
计数乘法近似值
Counting multiplicative approximations
论文作者
论文摘要
著名的猜想（1930年）涉及通过同一分母的理性近似两个实数，从而倍增了错误。在鲜为人知的论文中，Wang and Yu（1981）建立了一个用于此类近似数量的渐近公式，几乎总是有效的。使用Aistleitner-Borda-hauke的定量Koukoulopoulos--maynard定理，以及由Bohr集合理论引起的界限，我们推断出了对问题的不均匀和光纤精致的预期数量级的下限。
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.
