MATH Seminar

Title: Overconvergent differential operators acting on Hilbert modular forms
Seminar: Algebra
Speaker: Jon Aycock of University of California, San Diego
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-10-25 at 4:00PM
Venue: MSC N304
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Abstract: In 1978, Katz gave a construction of the $p$-adic $L$-function of a CM field by using a $p$-adic analog of the Maass--Shimura operators acting on $p$-adic Hilbert modular forms. However, this $p$-adic Maass--Shimura operator is only defined over the ordinary locus, which restricted Katz's choice of $p$ to one that splits in the CM field. In 2021, Andreatta and Iovita extended Katz's construction to all $p$ for quadratic imaginary fields using overconvergent differential operators constructed by Harron--Xiao and Urban, which act on elliptic modular forms. Here we give a construction of such overconvergent differential operators which act on Hilbert modular forms.