Harmonic Maass Forms of Weight One

Joint IAS/PU Number Theory Seminar
Topic:Harmonic Maass Forms of Weight One
Speaker:William Duke
Affiliation:University of California, Los Angeles
Date:Thursday, April 25
Time/Room:4:30pm - 5:30pm/Fine Hall 214

I will describe work with Yingkun Li on some arithmetic properties of the Fourier coefficients of harmonic modular forms of weight one. These are Maass forms of weight one whose eigenvalue under the Laplacian is zero and that are allowed to have polar-type singularities in the cusps. We show that in some dihedral cases they are connected to the Galois representations associated to newforms of weight one. We also find numerical evidence for this in several exotic cases.