Upper and lower bounds for higher moments of theta functions

2015/06/05 by Marc Munsch, Munsch, Marc, Igor E. Shparlinski +1 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1506.01999

arxiv created 2015/06/05 · arxiv updated 2015/06/08

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.

Cited by

• Lower bounds for high moments of zeta sums

Related

• Bounds for moments of quadratic character sums and theta functions
• High moments of theta functions and character sums
• A lower bound on high moments of character sums
• Lower bounds for moments of zeta and L-functions revisited
• Lower bounds for moments of zeta prime rho