University of Virginia
of Fourier coefficients of weak Maass forms
Abstract: In this talk, I will discuss recent work in
which we show that the
normalized Fourier coefficients of weak Maass forms of
prime level p become
equidistributed on [-1,1] as p goes to infinity. For
integral weight forms, these
coefficients are equidistributed with respect to the
Sato-Tate measure, while for
half-integral weight forms, these coefficients are
equidistributed with respect to
the arc length measure. The proofs involve a blend of
geometric and analytic methods.
This is joint work with Riad Masri.