题目：Large values of quadratic character sums

摘要：This talk concerns large values of quadratic Dirichlet character sums in the family of fundamental discriminants. Motivated by the P\'olya--Vinogradov inequality and by the work of Paley, Granville and Soundararajan, Hough, Munsch, and La Breteche--Tenenbaum, we study conditional Omega results for $\sum_{n\le |d|/x}\chi_d(n), X<|d|\le 2X,\quad d\in\mathcal F$. Under GRH, the resonance method yields lower bounds in complementary ranges of $x$, extending known large-value results for general character sums to the quadratic setting. The proof combines Polya's Fourier expansion, average estimates for quadratic characters, and different resonator constructions adapted to the relevant ranges.

报告人简介：王瑞华，海南比勒费尔德应用科学大学讲师，研究方向为解析数论与explicit Arakelov 几何。2018年硕士毕业于山东大学，师从刘建亚院士；2022年博士毕业于Leiden University，师从David Holmes与Robin de Jong。博士毕业后曾在华为从事6G与区块链相关研究，产出6项专利。2026年入选海南省E类人才与“四方引才”计划。

报告时间：6月15日 10：30-11：30

地点：知新楼B924

邀请人：王志伟 数学学院教授