Möbius orthogonality of sequences with maximal entropy

M{ö}bius orthogonality in density for zero entropy dynamical systems

It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $μ$ stands for the arithmetic M{ö}bius function, then there exists a subset $A$ of integers depending only on the system, of logarithmic density one, such that for each $f$ continuous on $X$, $\frac1N \sum_{n\leq N} f(T^nx)μ(n) \to 0$ as $N\to\infty$, $N\in A$, uniformly in $x\in X$. In particular, the density version of M{ö}bius orthogonality holds.

高秩退化Eisenstein级数的均值与量子方差

Mean Values and Quantum Variance for Degenerate Eisenstein Series of Higher Rank

本研究通过Watson-Ichino型公式和Jutila渐近公式，证明高秩退化Eisenstein级数平方内积的均值突破广义Lindelöf阈值，并计算量子方差，扩展了Zhang和Huang的工作。