On sup-norms of cusp forms of powerful level
Number Theory
2015-11-12 v4
Abstract
Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty <<_{\lambda, \epsilon} N^{-1/12 + \epsilon} for any \epsilon>0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree.
Keywords
Cite
@article{arxiv.1404.3179,
title = {On sup-norms of cusp forms of powerful level},
author = {Abhishek Saha},
journal= {arXiv preprint arXiv:1404.3179},
year = {2015}
}
Comments
Final version, to appear in JEMS. Please also note that the results of this paper have been significantly improved in my recent paper arXiv:1509.07489 which uses a fairly different methodology