ON-LINE: Number Theory Seminar

Speaker:  Shaul Zemel  (Hebrew University of Jerusalem)

Title: Shintani Lifts of Nearly Holomorphic Modular Forms

Abstract: The Shintani lift is a classical construction of modular forms of
half-integral weight from modular forms of even integral weight. Soon after
its definition it was shown to be related to integration with respect to
theta kernel. The development of the theory of regularized integrals opens
the question to what modular forms of half-integral weight arise as
regularized Shintani lifts of various kinds of integral weight modular
forms. We evaluate these lifts for the case of nearly holomorphic modular
forms, which in particular shows that when the depth is smaller than the
weight, the Shintani lift is also nearly holomorphic. This evaluation
requires the determination of certain Fourier transforms, which are
interesting on their own right. This is joint work with Yingkun Li.

Organisational information

Event: This seminar will take place online, as a Zoom meeting. Apart from the speaker, there will be a designated "host" of the event, whose job will be to moderate access, to collect the questions (that can be asked in the Zoom chat) and so on.

Participation: If you are not a member of the Algebra and Number Theory group of the University of Copenhagen, please send an email to the host. You will be added to the mailing list for this virtual seminar. Everyone in the mailing list will receive an email with the link to join the Zoom meeting approximately one hour before the starting time of the talk.