线性独立性准则的逆，几乎处处有效
A converse to linear independence criteria, valid almost everywhere
摘要：
我们证明了一个加权类似的欣钦-Groshev定理，其中最近的整数的距离被替换为绝对值。这是随后应用到证明的最优性的几个线性独立的标准领域的有理数。
英文摘要：
We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field of rational numbers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
