Academic Report of School of Mathematical Sciences [2026] No. 063

(Series Report for High-Level University Construction No. 1322)

Title：Piatetski-Shapiro primes in short intervals

Speaker：Zhenyu Guo, Associate Professor (Xi'an  Jiaotong University)

Time：10:00-11:00, June 24, 2026

Location：Room 2433, Huiwen Building, Yuehai Campus

Abstract: 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.

Speaker Profile：Zhenyu Guo is an associate professor in the School of Mathematics and Statistics at Xi’an Jiaotong University. His research focuses on analytic number theory. He received his Ph.D. from the University of Missouri–Columbia. From 2019 to 2020, he was a visiting scholar at the University of Illinois at Urbana-Champaign. He has received grants from the National Natural Science Foundation of China and the Provincial Natural Science Foundation. He has published more than twenty papers in journals such as the Journal of Number Theory and the Ramanujan Journal.

Faculty and students are welcome to attend!

Invited by: Yingnan Wang

School of Mathematical Sciences

June 22, 2026