Does anyone know of any papers which give results on the existence of Minkowski units in totally real cyclic fields of prime degree? F. Marko has some results for composite degree in his paper "On the existence of Minkowski units in totally real cyclic fields" but I'm more interested in the prime degree case. See https://www.emis.de/journals/JTNB/2005-1/pages195-206.pdf

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See this short note by Brumer and the book Elementary and Analytic Theory of Algebraic Numbers by Narkiewicz, in particular Section 3.3.