Root numbers for the Jacobian varieties of Fermat curves

Abstract

Let p be an odd prime number. Let K be the p-th cyclotomic field. We give general formulae for the root numbers of the Jacobian varieties of the Fermat curves Xp+Yp=δ where δ is an integer. As an application of these general formulae, we derive the equidistribution of the root numbers for the families of Jacobian varieties of the Fermat curves.