论文标题
Littlewood和Duffin-二聚体近似中的schaeffer型问题
Littlewood and Duffin--Schaeffer-type problems in diophantine approximation
论文作者
论文摘要
Gallagher的定理描述了典型载体的乘二磷酸近似值。我们建立了Gallagher定理的完全不均匀版本，二氧纤维的完善，以及Liouville纤维的鲜明而出乎意料的阈值。一路上，我们证明了一类非单调近似函数的达芬 - schaeffer猜想的不均匀版本。
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector. We establish a fully-inhomogeneous version of Gallagher's theorem, a diophantine fibre refinement, and a sharp and unexpected threshold for Liouville fibres. Along the way, we prove an inhomogeneous version of the Duffin--Schaeffer conjecture for a class of non-monotonic approximation functions.
