Joint IAS-PU Number Theory Seminar | |

Topic: | Sup-norms, Whittaker Periods and Hypergeometric Sums |

Speaker: | Nicolas Templier |

Affiliation: | Princeton University |

Date: | Thursday, February 9 |

Time/Room: | 4:30pm - 5:30pm/Fine Hall -- 214 |

We begin with a survey of recent results on the problem of bounding the sup-norm of automorphic forms. If f is a cuspidal automorphic forms on a reductive group G it is classical to study its value distribution and in the particular the maximum of |f(g)| for all g in G. Then we will explain an approach to this problem via Whittaker periods. We establish a new formula for non-archimedean Whittaker functions. The formula involves 2F1 hypergeometric sums and generalizes classical results of Casselman and others. As an application we disprove a folklore conjecture on the sup-norm of GL(2) modular forms.