Let X be a curve which is defined over a finite field k of characteristic p. We show that one can evaluate the discrete logarithm in Pic0(X)pn by O(n2 log p) operations in k. This generalizes a… (More)

A hyperelliptic function field can be always be represented as a real quadratic extension of the rational function field. If at least one of the rational prime divisors is rational over the field of… (More)

1 The Tate{Lichtenbaum pairing In the paper F-R] it is shown how the Tate pairing on Abelian varieties in Licht-enbaum`s version can be used to relate the discrete logarithm in the group J m (F q) of… (More)

In their famous article [Gr-Za], Gross and Zagier proved a formula relating heights of Heegner points on modular curves and derivatives of L-series of cusp forms. We prove the function field analogue… (More)