## Abstract

**1.** In 1947 R. Brauer [428] 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.

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