Generalizes Nagao conjecture to hyperelliptic curves, computes moments to obtain Jacobian rank 4g+2 over Q(T), and proves second-moment bias for some families.
Nagao, On the rank of elliptic curve y^2 = x^3 - kx , Kobe J
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Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture
Generalizes Nagao conjecture to hyperelliptic curves, computes moments to obtain Jacobian rank 4g+2 over Q(T), and proves second-moment bias for some families.