Séminaire d'arithmétique à Lyon

Fourier expansions at cusps

by Michalis Neururer (Darmstadt)

Salle M7 (UMPA, ENS de Lyon)

Salle M7

UMPA, ENS de Lyon


I will discuss the arithmetic significance of Fourier
expansions of modular forms at cusps. After a brief introduction of new
methods of calculating these expansions, I will talk about joint work
with F. Brunault, where we determine the number field generated by
Fourier coefficients of newforms at a cusp. Finally I will show work in
progress on bounding the denominators of Fourier expansions at cusps and
applications of these bounds to a conjecture on the Manin constants of
elliptic curves.

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