Norm bounds on Eisenstein series
Number Theory
2025-04-18 v3
Abstract
We study the sup-norm and mean-square-norm problems for Eisenstein series on certain arithmetic hyperbolic orbifolds, producing sharp exponents for the modular surface and Picard 3-fold. The methods involve bounds for Epstein zeta functions, and counting restricted values of indefinite quadratic forms at integer points.
Cite
@article{arxiv.2305.15162,
title = {Norm bounds on Eisenstein series},
author = {Dubi Kelmer and Alex Kontorovich and Christopher Lutsko},
journal= {arXiv preprint arXiv:2305.15162},
year = {2025}
}
Comments
13 pages. This version has been corrected to take into account the associated erratum