Abstract
The constants in the functional equation of the Artin
L
-function can be written as products of local root numbers and these in turn are defined in terms of local Galois Gauss sums. It is the arithmetic behaviour of the latter which is determined here in the tame case. In particular their ideal values are described by local resolvents, and two types of basic congruences are established. It is also shown that for a given local field the tame Galois Gauss sums can be characterized within that field by their arithmetic properties. In addition a new local proof for inductivity in the tame case is obtained.
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