Fourier Coefficients of Hilbert Modular Forms — Tim Davis (Northeastern University London)

In this talk we study the Fourier coefficients of Hilbert modular forms at cusps. Precisely, we study the number field which these coefficients generate. We will outline the proof of our result which uses an adelic approach and studies the algebraic properties of local Whittaker newforms. This generalises a result of Brunault and Neururer who proved the analogous result for modular forms using classical techniques.