On the semigroup of Artinʹs L-functions holomorphic at s0 Original Research Article

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