Westlake Online Math Forum第十二期 | Emmanuel Lecouturier: On the Harris--Venkatesh conjecture for weight one modular forms

2023-08-31 14:48:08


地点:E4-233 & ZOOM

ZOOM ID:921 6725 8223

PASSCODE: 064984

主讲人: 清华大学丘成桐数学科学中心, Emmanuel Lecouturier

主讲人介绍: Emmanuel Lecouturier joined Tsinghua University in 2018, he is an associate Professor at Yau Mathematical Science Center (YMSC). He is working on number theory (modular forms, elliptic curves, L-functions).

讲座主题:On the Harris--Venkatesh conjecture for weight one modular forms


In the spirit of general conjectures of Venkatesh on the action of derived Hecke operators on the cohomology of arithmetic groups, Harris and Venkatesh formulated a conjecture relating the action of certain derived Hecke operators on weight one eigenforms to a certain group of units in a number field. Much work has been done, by several authors, in the case of a dihedral weight one form. We will survey these results. Following the recent ideas of Robin Zhang, we will also motivate the conjecture from the perspective of special values of L-functions. This is based on the work of the author [IMRN 2023, DOI 10.1093/imrn/rnad119] and work in progress with Loïc Merel.