### The Fourier coefficients of Hilbert modular forms

Linfoot Number Theory Seminar

23rd November 2022, 11:00 am – 12:00 pm

Fry Building, Room 2.04

In this talk we give an answer to the following question: given a Hilbert newform and a matrix in the Hilbert modular group what is the explicit number field which contains all the Fourier coefficients of the Hilbert newform at that cusp? This generalises a result by Brunault and Neururer who answered this question in the setting of classical newforms. We will give an overview of the method used to prove our result which differs from the method of Brunault and Neuruer and relies on the properties of local Whittaker newforms.

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