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

 

Arithmetical paraphrases


Author: E. T. Bell
Journal: Trans. Amer. Math. Soc. 22 (1921), 1-30
MSC: Primary 11F99
MathSciNet review: 1501156
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  • [1] J. Liouville (1-18): Sur quelques formules générales qui peuvent être utiles dans la théorie des nombres. Eighteen memoirs, as follows: 1 to 6 in Journal de mathématiques pures et appliquées (2), vol. 3 (1858); 7 to 11 in vol. 4 (1859); 12 in vol. 5 (1860); 13 to 16 in vol. 9 (1864); 17, 18 in vol. 10 (1865). These will be referred to by citing the number of the memoir and the page.
  • [2] J. Liouville (19): Réponse de M. Liouville; Note de M. Liouville; ibid., vol. 7.
  • [2] 1. V. A. Lebesgue, ibid., vol. 7.
  • [3] H. J. S. Smith: Report on the Theory of Numbers (1865), (Collected Papers I), Art. 136.
  • [3] 1. C. M. Piuma, Giornale di Matematiche, vol. 4 (1866), 3 articles.
  • [3] 2. E. Fergola, Giornale di Matematiche, vol. 10 (1872).
  • [3] 3. G. Torelli, ibid., vol. 16 (1878).
  • [3] 4. S. J. Baskakov, Transactions of the Moscow Mathematical Society, vol. 10, I (1882-3).
  • [3] 5. T. Pepin, Accademia pontificia del nuovi Lincei, Atti, vol. 38 (1884-5).
  • [3] 6. N. V. Bougaief, Transactions of the Moscow Mathematical Society, vol. 12 (1885).
  • [4] T. Pepin: Sur quelques formules d'Analyse utiles dans la Théorie des nombres, Journal de mathématiques pures et appliquées, (4), vol. 4 (1888), pp. 83-131.
  • [5] T. Pepin: Sur quelques formes quadratiques quaternaires, ibid., vol. 6 (1890), pp. 1-67. This memoir illustrates one aspect of the usefulness of Liouville's methods.
  • [6] G. B. Mathews: On a theorem of Liouville's, Proceedings of the London Mathematical Society, vol. 25 (1893), pp. 85-92.
  • [7] W. Meissner: Inaugural Dissertation, Zürich, 1907. Followed by Bachmann in (8).
  • [8] P. Bachmann: Niedere Zahlentheorie, zweiter Teil, Additive Zahlentheorie, Leipzig (1910), pp. 365-433.
  • [9] G. Humbert, Bulletin des Sciences Mathématiques (2), vol. 34, I (1910).
  • [10] A. Deltour, Nouvelles Annales de Mathématiques (4), vol. 11 (1911).

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DOI: http://dx.doi.org/10.1090/S0002-9947-1921-1501156-4
PII: S 0002-9947(1921)1501156-4
Article copyright: © Copyright 1921 American Mathematical Society