Abstract
In this paper, we consider the generalized Hilbert symbol in a higher local field of charactersitic 0 with first residue field of characteristic 0 as well and with perfect last residue field of positive characteristic p, which originates from higher local p-class field theory developed by I. Fesenko. Using the descent to a subfield of mixed characteristic, from the generalized Artin-Hasse and Iwasawa formulas proved in a previous paper we deduce respective Artin-Hasse and Iwasawa explicit reciprocity laws in the case under consideration. Bibliography: 6 titles.
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