Trace series on Qk

Let K be a number field which contains [InlineMediaObject not available: see fulltext.] the absolute Galois group of K. Let [InlineMediaObject not available: see fulltext.] be the completion of [InlineMediaObject not available: see fulltext.] relative to the spectral norm [InlineMediaObject not available: see fulltext.]. A trace series and a trace function are associated to an element [InlineMediaObject not available: see fulltext.]. A measure preserving function H:G{inK}→[0,1] is constructed and a Fourier type theory is considered for elements of [InlineMediaObject not available: see fulltext.].