- 644 Downloads
1. In 1947 R. Brauer  found a proof of Artin’s conjecture on the divisibility of Dedekind zeta-functions for Galois extensions, showing first that in Artin’s theorem about linear combinations of characters induced by cyclic subgroups the rational coefficients may be taken to be nonnegative. As a corollary he obtained for normal extensions L / K a representation of \((\zeta _L(s)/\zeta _K(s))^n\) as a product of Abelian L-functions. He pointed out that from the truth of Artin’s conjecture on the integrality of Artin L-functions this corollary would hold also for non-normal extensions.