非齐次Duffin-Schaeffer猜想反例
Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture
AI总结：
本文构造逼近函数，证明非齐次Duffin-Schaeffer猜想对所有非零有理数和某些Liouville数不成立，给出反例。
AI中文摘要：
Duffin-Schaeffer猜想于2020年被证明，对于任意逼近函数，给出了用既约分数逼近无理数的零-全二分法。我们构造逼近函数，使得Duffin-Schaeffer猜想的非齐次类比失效。这些反例对所有非零有理数和某些Liouville数成立。
英文摘要：
The Duffin-Schaeffer Conjecture, proven in 2020, gives a zero-full dichotomy for the approximation of irrational numbers with reduced fractions for arbitrary approximation functions. We construct approximation functions such that the inhomogeneous analogue of the Duffin-Schaeffer Conjecture fails. The counterexamples are obtained for all non-zero rationals and certain Liouville numbers.
