群作用轨道上的素数与殆素数

Primes and almost primes on orbits of group actions

素数分布和不定方程是数论中两个古老的研究领域,也是推动现代数论发展的两个基本问题.近年来,代数、几何、分析和表示论充分地交叉融合,使得很多经典的问题有了新的视角.本文概述群作用轨道上的素数与殆素数分布相关问题的研究背景、内容及所涉及的研究方法.

The distribution of prime numbers and Diophantine equations are two ancient research topics in num-ber theory,serving as fundamental questions driving the development of modern number theory.In recent years,a thorough integration of algebra,geometry,analysis,and representation theory has provided new perspectives on many classical problems.In this paper,we provide an overview of the background,content,and methods involved in the study of the distribution of prime and almost prime on orbits of group actions.