Period polynomials of Bianchi modular forms

Abstract: Bianchi modular forms (i.e. automorphic forms over imaginary quadratic fields) share many similarities with their classical cousins. One such similarity is the period polynomial, studied for classical modular forms by Manin, Kohnen and Zagier, as well as many others. In this talk we define period polynomials of Bianchi modular forms, show how to compute them in practice, and use them to (conjecturally) extract information about congruences between Bianchi forms of various types (base-change and genuine forms; cusp forms and Eisenstein series). All of this is done through an example space of Bianchi forms, from which we find new congruences modulo 43 and 173. Time permitting, we will also describe some open problems relating to these methods, and how these relate to the classical picture. No prior knowledge of Bianchi modular forms is assumed.

number theory

Audience: researchers in the topic

London number theory seminar

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