TY - JOUR
T1 - Points on curves in small boxes and applications
AU - Chang, Mei Chu
AU - Cilleruelo, Javier
AU - Garaev, Moubariz Z.
AU - Hernández, José
AU - Shparlinski, Igor E.
AU - Zumalacárregui, Ana
PY - 2014/9/1
Y1 - 2014/9/1
N2 - We introduce several new methods to obtain upper bounds on the number of solutions of the congruences f (x) =y (mod p) and f (x) = y2(mod p), with a prime p and a polynomial f, where (x, y) belongs to an arbitrary square with side length M.We give two applications of these results to counting hyperelliptic curves in isomorphism classes modulo p and to the diameter of partial trajectories of a polynomial dynamical system modulo p.
AB - We introduce several new methods to obtain upper bounds on the number of solutions of the congruences f (x) =y (mod p) and f (x) = y2(mod p), with a prime p and a polynomial f, where (x, y) belongs to an arbitrary square with side length M.We give two applications of these results to counting hyperelliptic curves in isomorphism classes modulo p and to the diameter of partial trajectories of a polynomial dynamical system modulo p.
UR - http://www.scopus.com/inward/record.url?scp=84907058079&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP130100237
U2 - 10.1307/mmj/1409932631
DO - 10.1307/mmj/1409932631
M3 - Article
AN - SCOPUS:84907058079
SN - 0026-2285
VL - 63
SP - 503
EP - 534
JO - Michigan Mathematical Journal
JF - Michigan Mathematical Journal
IS - 3
ER -