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On the Mordell-Weil lattice of [Formula: see text] in characteristic 3

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We study the elliptic curves given by y 2 = x 3 + b x + t 3 n + 1 over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u 3... ...