Epstein zeta-functions, subconvexity, and the purity conjecture
Number Theory
2016-02-09 v1
Abstract
Subconvexity bounds are proved for general Epstein zeta functions of k-ary quadratic forms. This is related to sup-norm bounds for Eisenstein series on GL(k), and the exact sup-norm exponent is determined to be (k-2)/8 for k >= 2. In particular, if is odd, this exponent is not in Z/4, which shows that Sarnak's purity conjecture does not hold for Eisenstein series.
Keywords
Cite
@article{arxiv.1602.02326,
title = {Epstein zeta-functions, subconvexity, and the purity conjecture},
author = {Valentin Blomer},
journal= {arXiv preprint arXiv:1602.02326},
year = {2016}
}