Time：14:00-15:00, Wednesday, September 6 2023
ZOOM ID:921 6725 8223
PASSCODE:064984
Speaker：Emmanuel Lecouturier，YMSC
Biography: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).
Title：On the Harris--Venkatesh conjecture for weight one modular forms
Abstract:
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.
