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.
Serre, Topics in Galois Theory (Research Notes in Mathematics), A K Peters/CRC Press; 2 edition (November 2, 2007)
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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.