The Functional Equation for L-Functions of Hyperelliptic Curves

We compute the L-functions of a large class of algebraic curves and verify the expected functional equation numerically. Our computations are based on our previous results on stable reduction to calculate the local L-factor and the conductor exponent at the primes of bad reduction. We mainly restrict to the case of hyperelliptic curves of genus g ⩾ 2 defined over that have semistable reduction at every prime p. We also discuss a few more general cases to illustrate the usefulness of our method for general superelliptic curves.