References
Armitage, J.V.: Zeta functions with a zero ats=1/2. Inventiones math.15, 199–207 (1972).
Artin, E.: Zur Theorie derL-Reihen mit allgemeinen Gruppencharakteren. Collected papers (Ed. S. Lang and J. T. Tate). Reading: Addison-Wesley 1965.
Fröhlich, A.: On fields of class two. Proc. London Math. Soc. (3)4, 235–256 (1954).
Fröhlich, A.: The rational characterisation of certain sets of relatively Abelian extensions. Phil. Trans. Royal Soc. London, A251, 385–425 (1959).
Fröhlich, A.: A prime decomposition symbol for certain non-Abelian number fields. Acta Scient. Math. Hung.21, 229–246 (1960).
Lang, S.: Algebraic number theory. Reading: Addison-Wesley 1970.
Martinet, J.: Modules Sur l'Algèbre du Groupe Quaternionien. Ann. Sci. de l'Ec. Norm-Sup., 4e serie.4 (3), 399–408 (1971).
Rosenblüth, E.: Die arithmetische Theorie und Konstruktion der Quaternionenkörper auf Klassenkörpertheoretischer Grundlage. Monatsh. Math. Phys.41, 85–125 (1934).
Serre, J.-P.: Conducteurs d'Artin des caractères réels. Inventiones math.14, 173–183 (1971).
Weil, A.: Dirichlet series and automorphic forms. Lecture Notes in Mathematics189. Berlin-Heidelberg-New York: Springer 1971.
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Fröhlich, A. Artin-root numbers and normal integral bases for quaternion fields. Invent Math 17, 143–166 (1972). https://doi.org/10.1007/BF01418937
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DOI: https://doi.org/10.1007/BF01418937