A modified Gallagher's Lemma
Number Theory
2013-01-03 v1
Abstract
First we prove a modified version of the famous Lemma on the mean square estimate for exponential sums, by plugging the Cesaro weights in the right hand side of Gallagher's inequality. Then we apply it, in order to establish a mean value estimate for the Dirichlet polynomials.
Cite
@article{arxiv.1301.0008,
title = {A modified Gallagher's Lemma},
author = {Giovanni Coppola and Maurizio Laporta},
journal= {arXiv preprint arXiv:1301.0008},
year = {2013}
}
Comments
In the near future we'll study the generalization to "weighted Gallagher's Lemmas"