发表机构
Universität Zürich（苏黎世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对实线上具有共同压缩比的自相似测度乘积，证明了加权Khintchine-Schmidt定理的分形类似结果，通过提出锥提升方法，得到Khalil等人定理的部分有效形式。
AI 中文摘要
我们证明了实线上自相似测度乘积的加权Khintchine与Schmidt定理的分形类似结果，这些测度的定义迭代函数系统具有共同的压缩比。该证明将计数问题转化为齐次动力学，并基于Bénard、He和Zhang近期针对无加权情形的工作。我们的主要新要素是“锥提升”：针对乘积自相似测度平移的有效双重等分布定理，在权重属于正Weyl腔中固定锥的对角元上一致成立，该定理由单个权重的有效等分布推导而来。这得到了Khalil、Luethi和Weiss定理的部分有效形式。
英文摘要
We prove a fractal analogue of the weighted theorems of Khintchine and Schmidt for products of self-similar measures on the real line whose defining iterated function systems share a common contraction ratio. The proof translates the counting problem into homogeneous dynamics and builds on recent work of Bénard, He and Zhang, who treated the unweighted case. Our main new ingredient is a \emph{cone upgrade}: an effective double equidistribution theorem for translates of product self-similar measures, uniform over diagonal elements whose weights range over a fixed cone in the positive Weyl chamber, deduced from effective equidistribution for a single weight. This yields a partial effective form of a theorem of Khalil, Luethi and Weiss.
Comments34 pages, Comments welcome!
