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The behaviour of Galois Gauss sums with respect to restriction of characters Margolick, Michael William

Abstract

The theory of abelian and non-abelian L-functions is developed with a view to providing an understanding of the Langlands-Deligne local root number and local Galois Gauss sum. The relationship between the Galois Gauss sum of a character of a group and the Galois Gauss sum of the restriction of that character to a subgroup is examined. In particular a generalization of a theorem of Hasse-Davenport (1934) to the global, non-abelian case is seen to result from the relation between Galois Gauss sums and the adelic resolvents of Fröhlich.

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