AV研究所 学术报告[2026]063号

（高水平大学建设系列报告1322号)

报告题目：Piatetski-Shapiro primes in short intervals

报告人：郭振宇 副教授 （西安交通大学）

报告时间：2026年6月24日10:00-11:00

报告地点：粤海校区汇文楼2433

报告摘要：The existence of primes in a short interval, which asks if there are prime numbers in the interval $[x, x + x^\theta]$, is a core problem in number theory. Guth and Maynard proved the best known result for this problem with an asymptotic formula while Baker, Harman and Pintz proved the best lower bound result.

In this talk, I focus on Piatetski-Shapiro primes in a short interval. The study of Piatetski-Shapiro primes of the form $\lfloor n^c \rfloor$ is an approximation of the well-known conjecture that there exist infinitely many primes of the form $n^2+1$. I will  prove the existence of such primes under restrictions on $\theta$ and $c$ with an asymptotic formula and a lower bound, respectively. I will also present a short survey on recent progresses on Piatetski-Shapiro primes.

报告人简介：郭振宇，西安交通大学数学与统计学院副教授，研究方向为解析数论。博士毕业于美国密苏里大学哥伦比亚分校。2019-2020年在伊利诺伊大学厄巴纳香槟分校访问。曾获国家自然科学基金和省自然科学基金资助。已在《Journal of number theory》，《Ramanujan journal》等杂志发表二十余篇论文。

邀请人：王英男

AV研究所

2026年6月22日