Abstract: The question when a cusp form defined by a Poincaré series vanishes identically was recognized as interesting and complicated as early as 1882 by Poincaré himself. In 2009, G. Muić proved an integral non-vanishing criterion for Poincaré series on locally compact Hausdorff groups and used it to study the non-vanishing of various cusp forms of integral weight. In this talk, we present a strengthening of Muić's criterion and apply it to several classes of cuspidal automorphic forms on the metaplectic cover of \(\mathrm{SL}_2(\mathbb R) \), i.e., to the corresponding cusp forms of half-integral weight.
Integral non-vanishing criteria for Poincaré series
07.05.2019 13:15 - 14:15
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: