## On the functional equation of the Artin L-function for characters of real representations.(English)Zbl 0256.12010

### MSC:

 11R42 Zeta functions and $$L$$-functions of number fields 11S40 Zeta functions and $$L$$-functions
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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] Fröhlich, A.: Artin Root Numbers and Normal Integral Bases for Quaternion Fields. Inventiones math.17, 143-166 (1972). · Zbl 0261.12008 [3] Fröhlich, A.: The root numbers, conductors and representations of Artin for generalised quaternion groups. · Zbl 0321.12018 [4] Grothendieck, A.: Sém. Bourbaki 1964/65, exposé 279. [5] Lamprecht, E.: Allgemeine Theorie der Gaußschen Summen in endlichen kommutativen Ringen. Math. Nachn.9, 149-196 (1953). · Zbl 0050.04401 [6] Lang, S.: Algebraic Number Theory. Reading-London: Addison-Wesley 1970. · Zbl 0211.38404 [7] Serre, J.-P.: Conducteurs d’Artin des caractères réels. Inventiones math.14, 173-183 (1971). · Zbl 0229.13006
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