I will introduce a recent conjecture of Hayes concerning the value at s=0 of the
equivariant Artin L-function associated with an Abelian extension K/k of number fields. It
proposes a relationship between certain unramified Kummer extensions of K and the
denominators of the coefficients of this L-function value. The conjecture can be viewed as a
new generalization of the classical analytic class number formula.