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Transactions of the American Mathematical Society

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Congruence representations in algebraic number fields


Author: Eckford Cohen
Journal: Trans. Amer. Math. Soc. 75 (1953), 444-470
MSC: Primary 10.0X
DOI: https://doi.org/10.1090/S0002-9947-1953-0059308-X
MathSciNet review: 0059308
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  • [1] L. Carlitz, The singular series for sums of squares of polynomials, Duke Math. J. vol. 14 (1947) pp. 1105-1120. MR 0023304 (9:337b)
  • [2] -, Representations of arithmetic functions in $ GF[{p^n},x]$, Duke Math. J. vol. 14 (1947) pp. 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[{p^n},x]$, II, Duke Math. J. vol. 14 (1947) pp. 543-557. MR 0022233 (9:176b)
  • [5] -, Sums of an odd number of squares in $ GF[{p^n},x]$, Duke Math. J. vol. 15 (1948) pp. 501-511. MR 0025500 (10:16b)
  • [6] -, Rings of arithmetic functions, Duke Math. J. vol. 19 (1952) pp. 115-129. MR 0047072 (13:823d)
  • [7] -, Sur les fonctions arithmétiques relatives aux corps algébriques, C. R. Acad. Sci. Paris vol. 234 (1952) pp. 787-788. 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, Introduction to the theory of numbers, Oxford, 1938. MR 0067125 (16:673c)
  • [13] Helmut Hasse, Vorlesungen über Zahlentheorie, Berlin, 1950. 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. vol. 7 (1885) pp. 201-258. MR 1554684
  • [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. vol. 88 (1923) pp. 184-210. MR 1512127
  • [22] -, Sums of $ m$th powers of algebraic integers, Ann. of Math. vol. 46 (1945) pp. 313-339. MR 0012630 (7:49b)
  • [23] Albert Leon Whiteman, Additive prime number theory in real quadratic fields, Duke Math. J. vol. 7 (1940) pp. 208-232. MR 0003658 (2:250g)

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DOI: https://doi.org/10.1090/S0002-9947-1953-0059308-X
Article copyright: © Copyright 1953 American Mathematical Society

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