The $L^2$ restriction of the Eisenstein series to a geodesic segment
Abstract
We study the norm of the Eisenstein series restricted to a segment of a geodesic connecting infinity and an arbitrary real. We conjecture that on slightly thickened geodesics of this form, the Eisenstein series satifies restricted QUE. We prove a lower bound that matches this predicted asymptotic. We also prove an upper bound that nearly matches the lower bound assuming the Riemann Hypothesis (unconditionally, the sharp upper bound holds for almost all ). Finally, we show the restricted QUE conjecture for geodesics with rational endpoints.
Keywords
Cite
@article{arxiv.1508.01470,
title = {The $L^2$ restriction of the Eisenstein series to a geodesic segment},
author = {Matthew P. Young},
journal= {arXiv preprint arXiv:1508.01470},
year = {2017}
}
Comments
The results in this paper are superseded by my new paper, "Equidistribution of Eisenstein series on geodesic segments." In particular, the main conjecture in this paper is proved there, in an even stronger form