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Arithmetische Eigenschaften von Galois-Räumen. I. (German) Zbl 0126.17002


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[1] Birman, A.: On the existence of a co-relation between two unsolved problems in number theory. Riveon Lematematika13, 17-19 (1959).
[2] Davenport, H., u.H. Hasse: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. reine angew. Math.172, 151-182 (1935). · JFM 60.0913.01 · doi:10.1515/crll.1935.172.151
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[5] – Theoria residuorum biquadraticorum. Commentat. soc. regiae sc. Gottingensis rec.,6 (1828); Werke, Bd. II, 67-92. Lipsiae: Fleischer 1863.
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[12] Lebesgue, V. A.: Recherches sur les nombres, § I. J. math. pures appl.2, 253-292 (1837).
[13] ?? Recherches sur les nombres, § II. J. math. pures appl.3, 113-144 (1838). · ERAM 018.0597cj
[14] Mann, H. B.: Analysis and Design of Experiments. New York: Dover Publ. 1949. · Zbl 0033.02803
[15] Nagell, T.: Introduction to number theory. New York: Wiley 1951. · Zbl 0042.26702
[16] Roquette, P.: Arithmetischer Beweis der Riemannschen Vermutung in Kongruenz-funktionenkörpern beliebigen Geschlechtes. J. reine angew. Math.191, 199-252 (1953). · Zbl 0051.27303 · doi:10.1515/crll.1953.191.199
[17] Salmon, G.: Lessons introductory to the modern higher algebra. 4th ed. Dublin: Hodges Figgis & Co. 1885.
[18] Scarpis, U.: Intorno alla risoluzione per radicali di un’equazione algebrica in un campo di Galois. Per. di Mat. (3)9, 73-79 (1912). · JFM 42.0117.03
[19] ?? Intorno all’interpretazione della Teoria di Galois in un campo di razionalità finito. Ann. di Mat. (3)23, 41-60 (1914). · JFM 45.0185.05
[20] Segre, B.: The non-singular cubic surfaces. Oxford: The Clarendon Press 1942. · Zbl 0061.36701
[21] ?? The biaxial surfaces, and the equivalence of binary forms. Proc. Cambridge Phil. Soc.41, 187-209 (1945). · Zbl 0063.06862 · doi:10.1017/S030500410002257X
[22] ?? Equivalenza ed automorfismi delle forme binarie in un dato anello o campo numerico. Rev. Univ. Nac. Tucuman5, 7-68 (1946). · Zbl 0063.06866
[23] ?? Lezioni di geometria moderna. Vol. I. Bologna: Zanichelli 1948. · Zbl 0030.41005
[24] ?? Intorno alla geometria sopra un campo di caratteristica due. Rev. Fac. Sc. Univ. Istanbul, (A)21, 97-123 (1956). · Zbl 0073.36802
[25] ?? Le geometrie di Galois. Ann. di Mat. (4)48, 1-96 (1959). · Zbl 0093.33604 · doi:10.1007/BF02410658
[26] ?? Lectures on modern geometry. Roma: Cremonese 1961. · Zbl 0095.14802
[27] ?? Geometry and algebra in Galois spaces. Abhandl. math. Seminar hamburg. Univ.25, 129-139 (1962). · Zbl 0106.35603 · doi:10.1007/BF02992923
[28] Weil, A.: Sur les courbes algébriques et les variétés qui s’en déduisent. Paris: Hermann 1948. · Zbl 0036.16001
[29] ?? Numbers of solutions of equations in finite fields. Bull. Am. Math. Soc.55, 497-508 (1949). · Zbl 0032.39402 · doi:10.1090/S0002-9904-1949-09219-4
[30] Der Satz von Nr. 3 findet sich mit einer anderen Ableitung bereits beiL. Carlitz: An application of a theorem of Stickelberger. Simon Stevin31, 27-30 (1956). Der Fallq=p war schon früher (mit Hilfe der Idealtheorie) erledigt worden vonL. Stickelberger, Verh. 1. Internat. Math.-Kongreß, Zürich 1897, 182-193. Leipzig: Teubner 1898; Vgl. auch:Th. Skolem: On a certain connection between the discriminant of a polynomial and the number of its irreducible factors modp. Norsk Mat. Tidsskr.34, 81-85 (1952).
[31] Der Satz von Nr. 60 wurde schon direkt bewiesen vonS. Chowla: A property of biquadratic residues. Proc. Nat. Acad. Sci. India, Sec. A,14, 45-46 (1944); vgl. außerdem auchE. Lehmer: On residue difference sets. Canad. J. Math.5, 425-432 (1953).
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