AI 中文总结
该综述围绕解析数论中一类误差项的矩展开，回顾了狄利克雷除数问题等的矩，给出\(\Delta_2(x)\)和\(\Delta_3(x)\)符号变化联合分布新结果，还对塞尔伯格类中矩结果提出猜想。
AI 中文摘要
本文是关于解析数论中一类误差项矩的综述文章。首先回顾了狄利克雷除数问题的矩，接着回顾了除数问题中误差项的混合矩。给出了关于\(\Delta_2(x)\)和\(\Delta_3(x)\)符号变化联合分布的两个新结果。最后给出了关于著名塞尔伯格类中矩结果的一些猜想。
英文摘要
This is a survey article on the moments of a class of error terms in analytic number theory. We begin by reviewing the moments of the Dirichlet divisor problem, and then review the hybrid moments of error terms in the divisor problems. We give two new results on the joint distribution of sign changes of $Δ_2(x)$ and $Δ_3(x). $ In the last section, we present some conjectures on the moment results in the well-known Selberg class.
Journal refAdvances in Mathematics (China), Vol. 55(2026), 481-504
