School of Mathematical Sciences Academic Report [2025] 049

(High-Level University Construction Series Report No. 1071)

Lecture Title: Continuous lower bounds for moments of the mixed product of twisted L-functions

Speaker: Assoc. Prof. Guohua Chen (North China University of Water Resources and Electric Power)

Date & Time: 4:30 - 5:00 PM, June 23, 2025

Venue: Room 2433, Convergence Building

Abstract: Moments of central values in families of L-functions are important topics in analytic number theory. Thanks to the important work of Keating and Snaith etc., there have been some well-established conjectured asymptotic formulas. However, one can verify the conjectured asymptotic formulas are true only for few families of L-functions. So far, establishing the correct order of magnitude of lower bounds is out of reach for many families of L-functions. In this talk, we will introduce the lower bound principle of Heap and Soundararajan, then use this principle to obtain sharp lower bounds for all positive real k-th (k > 1) moments of the mixed product of two twisted L-functions at the central value, which extend the previous results. This is a joint work with Weiping Li and Tianze Wang.

Biography: Guohua Chen, Associate Professor and Master’s Supervisor at North China University of Water Resources and Electric Power, obtained his PhD from Shandong University in 2018. From September 2016 to September 2017, he conducted joint doctoral training at the University of Göttingen (Germany) under Prof. Valentin Blomer with support from the Chinese government scholarship. He has led one National Natural Science Foundation of China (NSFC) Youth Program, one Henan Provincial Natural Science Foundation Youth Program, and one Key Research Project of Henan Higher Education Institutions. With over 10 publications in journals including J. Number Theory and Ramanujan J., he co-received the Third Prize of Henan Provincial Natural Science Award.

All faculty and students are welcome to attend!

Invited by: Yingnan Wang

School of Mathematical Sciences

June 22, 2025