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Zeta functions with a zero at \(s = \frac12\). (English) Zbl 0233.12006


MSC:

11R42 Zeta functions and \(L\)-functions of number fields

References:

[1] Armitage, J. V.: On a theorem of Hecke in number fields and function fields. Inventiones math.2, 238-246 (1967). · Zbl 0143.06304 · doi:10.1007/BF01425516
[2] Cassels, J. W. S., Fröhlich, A. (eds.): Algebraic number theory. London and New York: Academic Press 1967. · Zbl 0153.07403
[3] Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebras. New York: Wiley 1966. · Zbl 1093.20003
[4] Fröhlich, A.: Some topics in the theory of module conductors. Oberwolfach reports,2, 59-82 (1965).
[5] Hasse, H.: Zur Theorie der abstrakten elliptischen Funktionenkörper III. Journ. f. Math.175, 193-208 (1936). · Zbl 0014.24902
[6] Hasse, H.: Artinsche Führer, ArtinscheL-Funktionen und Gausssche Summen. Acta Salmanticensia, Ciencias: Sec. Mat. 1954. · Zbl 0057.27305
[7] Lamprecht, E.: Allgemeine Theorie der Gausschen Summen in endlichen kommutativen Ringen. Math. Nachr.9, 150-196 (1953). · Zbl 0050.04401 · doi:10.1002/mana.19530090303
[8] Lang, S.: Algebraic number theory. Reading, Mass: Addison-Wesley 1970 · Zbl 0211.38404
[9] Serre, J.-P.: Corps Locaux (deuxième édition). Paris: Hermann 1968.
[10] Serre, J.-P.: Représentations Linéaires des Groupes Finis. Paris: Hermann 1967.
[11] Serre, J.-P.: Conducteurs d’Artin des caractères réels. Inventiones math.14, 173-183 (1971). · Zbl 0229.13006 · doi:10.1007/BF01418887
[12] Weil, A.: Dirichlet series and automorphic forms. Lecture Notes in Mathematics189, Berlin-Heidelberg-New York: Springer 1971. · Zbl 0218.10046
[13] Weil, A.: Numbers of solutions of equations in finite fields. Bull. Amer. Math. Soc.55, 497-508 (1949). · Zbl 0032.39402 · doi:10.1090/S0002-9904-1949-09219-4
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