Upper and lower bounds for higher moments of theta functions
Marc Munsch, Igor E. Shparlinski
TL;DR
This paper establishes optimal lower bounds and new upper bounds for moments of theta functions, advancing understanding of their behavior through bounds on character sums and recent analytical techniques.
Contribution
It provides the first optimal lower bounds for theta function moments and introduces improved upper bounds on individual and average theta values.
Findings
Optimal lower bounds for theta function moments.
New upper bounds on individual theta values.
Enhanced bounds on moments over primes.
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.
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