TY - JOUR
T1 - On solutions to some polynomial congruences in small boxes
AU - Shparlinski, Igor E.
N1 - Copyright the Publisher 2013. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.
PY - 2014/4
Y1 - 2014/4
N2 - We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime p. In particular, we obtain nontrivial results about the number of solutions in boxes with the side length below p1/2, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.
AB - We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime p. In particular, we obtain nontrivial results about the number of solutions in boxes with the side length below p1/2, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.
UR - http://www.scopus.com/inward/record.url?scp=84902159257&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP130100237
U2 - 10.1017/S0004972713000671
DO - 10.1017/S0004972713000671
M3 - Article
AN - SCOPUS:84902159257
VL - 89
SP - 300
EP - 307
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
SN - 0004-9727
IS - 2
ER -