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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Congruence representations in algebraic number fields


Author: Eckford Cohen
Journal: Trans. Amer. Math. Soc. 75 (1953), 444-470
MSC: Primary 10.0X
MathSciNet review: 0059308
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  • [1] L. Carlitz, The singular series for sums of squares of polynomials, Duke Math. J. 14 (1947), 1105–1120. MR 0023304 (9,337b)
  • [2] L. Carlitz, Representations of arithmetic functions in 𝐺𝐹[𝑝ⁿ,𝑥], Duke Math. J. 14 (1947), 1121–1137. MR 0023305 (9,337c)
  • [3] R. D. Carmichael, Expansions of arithmetical functions in infinite series, Proc. London Math. Soc. (2) vol. 34 (1932) pp. 1-26.
  • [4] Eckford Cohen, Sums of an even number of squares in 𝐺𝐹[𝑝ⁿ,𝑥]. II, Duke Math. J. 14 (1947), 543–557. MR 0022233 (9,176b)
  • [5] Eckford Cohen, Sums of an odd number of squares in 𝐺𝐹[𝑝ⁿ,𝑥], Duke Math. J. 15 (1948), 501–511. MR 0025500 (10,16b)
  • [6] Eckford Cohen, Rings of arithmetic functions, Duke Math. J. 19 (1952), 115–129. MR 0047072 (13,823d)
  • [7] Eckford Cohen, Sur les fonctions arithmétiques relatives aux corps algébriques, C. R. Acad. Sci. Paris 234 (1952), 787–788 (French). MR 0047073 (13,823e)
  • [8] -, A finite analog of the Goldbach problem, not yet published.
  • [9] Leonard Eugene Dickson, Linear groups, Leipzig, 1901.
  • [10] -, Algebras and their arithmetics, Chicago, 1923.
  • [11] A. A. Fraenkel, Über die Teiler der Null und die Zerlegung von Ringen, J. Reine Angew. Math. vol. 145 (1914) pp. 139-176.
  • [12] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125 (16,673c)
  • [13] Helmut Hasse, Über den algebraischen Funktionenkörper der Fermatschen Gleichung, Acta Univ. Szeged. Sect. Sci. Math. 13 (1950), 195–207 (German). MR 0039008 (12,482f)
  • [14] E. Hecke, Vorlesungen über die Theorie der algebraischen Zahlen, Leipzig, 1923.
  • [15] Camille Jordan, Traité des substitutions, Paris, 1870.
  • [16] Jakob Klotz, Anzahl der Lösungen einer quadratischen Kongruenz in einem beliebigen endlichen algebraischen Zahlkörper, Vierteljahrschrift der Naturforschende Gesellschaft in Zürich vol. 58 (1913) pp. 239-268.
  • [17] Edmund Landau, Vorlesungen über Zahlentheorie, vol. I, Leipzig, 1927.
  • [18] Hermann Minkowski, Untersuchungen über quadratische Formen, Acta Math. 7 (1885), no. 1, 201–258 (German). I. Bestimmung der Anzahl verschiedener Formen, welche ein gegebenes Genus enthält. MR 1554684, http://dx.doi.org/10.1007/BF02402203
  • [19] Oystein Ore, Les corps algébriques et la théorie des idéaux, Paris, 1934.
  • [20] Hans Rademacher, Zur additive Primzahltheorie algebraischer Zahlkörper, III, Math. Zeit. vol. 27 (1928) pp. 319-426.
  • [21] Carl Ludwig Siegel, Additive Theorie der Zahlkörper. II, Math. Ann. 88 (1923), no. 3-4, 184–210 (German). MR 1512127, http://dx.doi.org/10.1007/BF01579178
  • [22] Carl Ludwig Siegel, Sums of 𝑚th powers of algebraic integers, Ann. of Math. (2) 46 (1945), 313–339. MR 0012630 (7,49b)
  • [23] Albert Leon Whiteman, Additive prime number theory in real quadratic fields, Duke Math. J. 7 (1940), 208–232. MR 0003658 (2,250g)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1953-0059308-X
PII: S 0002-9947(1953)0059308-X
Article copyright: © Copyright 1953 American Mathematical Society