TY - JOUR
T1 - Upper and lower bounds for higher moments of theta functions
AU - Munsch, Marc
AU - Shparlinski, Igor E.
PY - 2016/3
Y1 - 2016/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84962592809&partnerID=8YFLogxK
U2 - 10.1093/qmath/hav039
DO - 10.1093/qmath/hav039
M3 - Article
AN - SCOPUS:84962592809
SN - 0033-5606
VL - 67
SP - 53
EP - 73
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1
ER -