Graduate Number Theory Seminar

Title: Shimura lifts of almost holomorphic modular forms

Abstract: Shimura established a correspondence between some modular forms of weight k+1/2 and ones of weight 2k, known as the Shimura lift. Selberg showed that for some Hecke eigenforms f of integer weight k, the Shimura lift of f(4z)θ(z) takes on a particularly nice form: f(z)^2. In 2024, this identity was generalized from products to Rankin–Cohen brackets, and I will show how to generalize this even further after extending the Shimura lift to almost holomorphic modular forms.