Upper and Lower Bounds for Higher Moments of Theta Functions

Marc Munsch, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)53-73
Number of pages21
JournalThe Quarterly Journal of Mathematics
Issue number1
Publication statusPublished - 8 Dec 2014
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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