On the semigroup of Artin's L-functions holomorphic at s0

Let K/Q be a finite Galois extension, and let s0≠1 be a complex number. We prove that the multiplicative semigroup of Artin L-functions in K/Q which are holomorphic at s0 is finitely generated. We obtain a criterion for Artin's conjecture and we discuss the case of icosahedral extensions.