Quinary forms and paramodular forms

Abstract: The goal of this talk is to explain how one can use orthogonal modular forms to find and prove congruences between paramodular forms.

In the first part of the talk I will give a brief review of orthogonal modular forms and how the case of SO(5) can be used to compute paramodular forms, based on recent work of Rama-T, Rösner-Weissauer, Dummigan-Pacetti-Rama-T.

In the second part of the talk I will explain how we use orthogonal modular forms to prove congruences of paramodular forms, including examples of Fretwell and of Golyshev. A key ingredient for this is the unexpected appearance of orthogonal eigenforms which /do not/ correspond to paramodular forms (see Rama-T in ANTS 2020).

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

Series comments: This is part of the University of Bristol's Heilbronn number theory seminar. If you wish to attend the talk (and are not a Bristolian), please register using this form or email us at bristolhnts@gmail.com with your name and affiliation (if any).

We will email out the link to all registered participants the day before.