Über Relationen zwischen Artinschen L-Funktionen. (On relations between Artin L-functions) (Q2640654)

After a concise summary of the main properties of Artin L-functions, the author investigates arithmetical consequences of the classical theorem of Artin's on multiplicative independence of these L-functions. In his four theorems, somewhat technical to be stated here precisely, the multiplicative relations between the L-functions for a finite normal extension with the Galois group G are expressed in terms of certain G- modules. It is noted that some of the results bear a connection to the embedding problem for number fields. As a corollary to one of the theorems, the author proves that if the L-functions for a normal extension are not multiplicatively independent, then not every conjugacy class in its Galois group contains a Frobenius automorphism, corresponding to a prime completely inert in this extension.