Norm bounds on Eisenstein series
arXiv:2305.15162
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.
13 pages. This version has been corrected to take into account the associated erratum