Points on Curves in Small Boxes and Applications
نویسندگان
چکیده
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) ≡ y (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.
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