题    目：On joint moments of higher order derivatives of CUE characteristic polynomials

主讲人：魏菲

单    位：英国萨塞克斯大学

时    间：2024年7月13日 9:00

地    点：数学与统计学院207教室

摘    要：In this talk, I will introduce the asymptotic formulae for joint moments of higher order derivatives of CUE characteristic polynomials. These formulae are expressed in terms of determinants whose entries involve modified Bessel functions of the first kind. Similar results are obtained for the analogue of Hardy's Z-function. I will use these formulae to formulate general conjectures for the joint moments of higher order derivatives of the Riemann zeta-function and of Hardy's Z-function. The conjectures are supported by comparison with results obtained previously in the number theory literature.

简    介：魏菲，2011年本科毕业于河南大学，2018年在美国新罕布什尔大学取得博士学位，现任英国萨塞克斯大学研究助理。主要研究方向是解析数论，曾先后在哈佛大学、清华大学、牛津大学从事博士后研究工作。