On the local $L^2$ -Bound of the Eisenstein series

Abstract

We study the growth of the local $L^2$ -norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a poly-logarithmic bound on an average, for a large class of reductive groups. The method is based on Arthur’s development of the spectral side of the trace formula, and ideas of Finis, Lapid and Müller.

Keywords

• 11F70
• 11F72
• 22E55