arXiv subjects

Xiaoguang He

Publications and source records attributed to Xiaoguang He.

3 recordsLinked to original sources

arXiv2022

Discorrelation of multiplicative functions with nilsequences and its application on coefficients of automorphic $L$-functions

We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic $L$-function on $GL_m (m \geq 2)$ and polynomial nilsequences has logarithmic decay; the other is that the mean value of the Möbius function, coefficients of automorphic $L$-function and polynomial nilsequences also has logarithmic decay.

math.NT↗

arXiv2021

Bounds for moments of modular $L$-functions to a fixed modulus

We study the $2k$-th moment of the family of twisted modular $L$-functions to a fixed prime power modulus at the central values. We establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$.

math.NT↗

arXiv2019

Möbius Disjointness for Nilsequences Along Short Intervals

For a nilmanifold $G/Γ$, a $1$-Lipschitz continuous function $F$ and the Möbius sequence $μ(n)$, we prove a bound on the decay of the averaged short interval correlation $$\frac1{HN}\sum_{n\leq N}\Big|\sum_{h\leq H} μ(n+h)F(g^{n+h}x)\Big|$$ as $H,N\to\infty$. The bound is uniform in $g\in G$, $x\in G/Γ$ and $F$.

math.DS↗