# Pavel Guerzhoy

Affiliation: University of Hawaii

Email: pavel@math.hawaii.edu

Title Of Talk: Half-integral weigh $p$-adic coupling

Abstract: For a weakly holomorphic Hecke eigenform of even integral weight, one applies Atkin's $U$-operator repeatedly. The $p$-adic limit exists as a $q$-series and can be identified with a certain holomorphic Hecke eigenform. We present a parallel result which requires a very different proof for a half-integral weight eigenform. This is a joint project with K. Bringmann and B. Kane.