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Fourier coefficients of Automorphic forms

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NC2W02 - Crossing the bridge: New connections in number theory and physics

We will define the notion of Fourier coefficients of automorphic forms, and describe results and conjectures on them. In more detail, to every automorphic form on a group G and every rational nilpotent orbit in the Lie algebra of G, one attaches a function on the adelic points of G, called the Fourier coefficient. Actually, there are several ways to attach a Fourier coefficient of the same form to the same orbit, and we will describe some relations between them. We will discuss some results and conjectures regarding the set of orbits such that the corresponding coefficient is non-zero. If time permits, we will discuss a relation between Fourier coefficients and other automorphic periods.

This talk is part of the Isaac Newton Institute Seminar Series series.

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