Points on curves in small boxes and applications

Mei Chu Chang, Javier Cilleruelo, Moubariz Z. Garaev, José Hernández, Igor E. Shparlinski, Ana Zumalacárregui

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)503-534
Number of pages32
JournalMichigan Mathematical Journal
Volume63
Issue number3
DOIs
Publication statusPublished - 1 Sep 2014
Externally publishedYes

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