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Artin-root numbers and normal integral bases for quaternion fields. (English) Zbl 0261.12008


MSC:

11R42 Zeta functions and \(L\)-functions of number fields
11R18 Cyclotomic extensions
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References:

[1] Armitage, J.V.: Zeta functions with a zero ats=1/2. Inventiones math.15, 199-207 (1972). · Zbl 0233.12006
[2] Artin, E.: Zur Theorie derL-Reihen mit allgemeinen Gruppencharakteren. Collected papers (Ed. S. Lang and J. T. Tate). Reading: Addison-Wesley 1965.
[3] Fröhlich, A.: On fields of class two. Proc. London Math. Soc. (3)4, 235-256 (1954). · Zbl 0055.03301
[4] Fröhlich, A.: The rational characterisation of certain sets of relatively Abelian extensions. Phil. Trans. Royal Soc. London, A251, 385-425 (1959). · Zbl 0098.03402
[5] Fröhlich, A.: A prime decomposition symbol for certain non-Abelian number fields. Acta Scient. Math. Hung.21, 229-246 (1960). · Zbl 0117.27401
[6] Lang, S.: Algebraic number theory. Reading: Addison-Wesley 1970. · Zbl 0211.38404
[7] Martinet, J.: Modules Sur l’Algèbre du Groupe Quaternionien. Ann. Sci. de l’Ec. Norm-Sup., 4e serie.4 (3), 399-408 (1971). · Zbl 0219.12012
[8] Rosenblüth, E.: Die arithmetische Theorie und Konstruktion der Quaternionenkörper auf Klassenkörpertheoretischer Grundlage. Monatsh. Math. Phys.41, 85-125 (1934). · Zbl 0009.39202
[9] Serre, J.-P.: Conducteurs d’Artin des caractères réels. Inventiones math.14, 173-183 (1971). · Zbl 0229.13006
[10] Weil, A.: Dirichlet series and automorphic forms. Lecture Notes in Mathematics189. Berlin-Heidelberg-New York: Springer 1971.
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