Document Zbl 0261.12008

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

Invent. Math. 17, 143-166 (1972).

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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 · doi:10.1007/BF01404125
[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 · doi:10.1112/plms/s3-4.1.235
[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 · doi:10.1098/rsta.1959.0007
[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 · doi:10.1007/BF01697851
[9]	Serre, J.-P.: Conducteurs d’Artin des caractères réels. Inventiones math.14, 173-183 (1971). · Zbl 0229.13006 · doi:10.1007/BF01418887
[10]	Weil, A.: Dirichlet series and automorphic forms. Lecture Notes in Mathematics189. Berlin-Heidelberg-New York: Springer 1971.

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