Upper and lower bounds for higher moments of theta functions
Number Theory
2015-06-08 v1
Abstract
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of character sums and in particular on a modification of some recent results of M. Z. Garaev.
Cite
@article{arxiv.1506.01999,
title = {Upper and lower bounds for higher moments of theta functions},
author = {Marc Munsch and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1506.01999},
year = {2015}
}