# Bounds at s=1 for an axiomatic class of L-functions

Presented by:
G Molteni [Milan]
Date:
Friday 16th July 2004 - 17:30 to 17:50
Venue:
INI Seminar Room 1
Session Title:
Matrix Ensembles and L-Functions
Abstract:

When the Ramanujan hypothesis about the Dirichlet coefficients of a generic L-function is assumed, it is quite easy to prove upper-bounds of type L(1)<< R^c, for every c>0, where R is a parameter related to the functional equation of L. We show how to prove the same bound when the Ramanujan hypothesis is replaced by a much weaker assumption and L has Euler product of polynomial type. As a consequence, we obtain an upper bound of this type for every cuspidal automorphic GL(n) L-function, unconditionally. We employ these results to obtain Siegel-type lower bounds for twists by Dirichlet characters of the symmetric cube of a Maass form.

Presentation Material: