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


11R42 Zeta functions and \(L\)-functions of number fields
11R18 Cyclotomic extensions
Full Text: DOI EuDML


[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.