(joint work with Mei-Chu Chang, Javier Cilleruelo, Moubariz Garaev.
Jose Hernandez and
For a prime p , we obtain non-trivial upper bounds for the number of hyperelliptic curves
Y2 = X2g+1 + a2g-1 X2g-1 + ... + a1 X + a0
over Fp, with coefficients in a 2g-dimensional cube
(a0, ..., a2g-1) ∈ [R0+1, R0+M] × ... × [R2g-1+1, R2g-1+M]
that are isomorphic to a given curve and give an almost sharp lower bound on the number
of non-isomorphic hyperelliptic curves with coefficients in that cube.