The theory of Hecke L-series was unified and simplified in the first application of adelic functional analysis, carried out in Tate's thesis [\textit{J. Tate}, ``Fourier analysis in number fields and Hecke's zeta function'' (Ph. D. thesis, Princeton Univ. 1950)] and noted simultaneously and independently by \textit{K. Iwasawa} at the 1950 International Congress [``A note on functions'', Proc. Internat. Congr. Math., Cambridge 1950, Vol. 1, 322 (1952)]. From the viewpoint of a more general theory of zeta functions associated to representations of algebraic groups, the Iwasawa-Tate zeta function may be considered to be the zeta function associated to the representation of \(Gl_ 1\) on the line by multiplication. This paper develops the theory of the zeta functions associated to the other representations of \(Gl_ 1\), where \(t\in Gl_ 1\) acts on x by \(t^ nx\), for a fixed integer \(n\geq 2\). The zeta functions for these representations are shown to be expressible in terms of the original Iwasawa-Tate zeta function. In the case \(n=2\), an application of this zeta function analysis to the study of discriminants of quadratic extensions of global fields is presented.