时间：2026年5月26日（周二）14:00-15:00
地点：E14-301
报告人：Emmanuel Royer, Université Clermont Auvergne
报告人简介: Professor Emmanuel Royer is a full professor at Université Clermont Auvergne, currently seconded to the Centre National de la Recherche Scientifique (CNRS) to lead the International Research Laboratory CRM-CNRS (Montreal, Quebec, Canada). He holds a PhD from Université Paris-Saclay, where he completed his dissertation in 2001.
He began his career at Université Paul Valéry Montpellier before being appointed professor at Université Clermont Auvergne in 2006. There, he served as director of the Blaise Pascal Mathematics Laboratory before joining the CNRS leadership from 2018 to 2023 as Deputy Scientific Director. He has been directing the CRM-CNRS since September 2024.
His research primarily focuses on modular forms and their generalizations, as well as L-functions. He approaches these topics from both analytical and algebraic perspectives.
报告主题：A formula for a weighted mean of Dirichlet L-functions
报告摘要：We wish to present a recent work done with Sébastien Darses and Berend Ringeling. We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties—including Eisenstein series and period functions—that were originally introduced and studied by Lewis and Zagier, and later by Bettin and Conrey in the case of the Riemann zeta function, and more recently by Lewis and Zagier for odd real characters. These tools yield closed-form expressions for the moments of a measure defined via a weighted mean square of the L-function. These moments not only provide a complete characterization of the modulus of the L-function on the critical line, but also imply an infinite number of non-trivial positivity conditions valid for all primitive characters, real or not.
