The functional equation for L-functions of hyperelliptic curves

2015/04/02 by Börner, Michel, Bouw, Irene I., Wewers, Stefan · 1 citation
#11G20 #11G40 #14G10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1504.00508

Abstract

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. Most of our examples are hyperelliptic curves of genus g≥ 2 defined over ℚ which have semistable reduction at every prime p. We also treat a few more general examples of superelliptic curves.

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