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Annali di Matematiea pura ed applieata, serie 22, vol. 13, pp. 235–351; reprinted inExcursions arithmétiques à l' infini, pp. 104–117, Paris, 1885; also elsewhere, cf. references inDickson's:History of the Theory of Numbers, vol. I (Washington, D. C., 1919).
It is inexact to say that the functions (2) form an abeliangroup. Thus, for example, if α is prime, ε x (x) has no inverse in the set (2).Cesàro, (Annali, vol. 14, p. 155), calls (2) agroupe fermé; the nomenclature here employed is in accordance with modern usage. Likewise forCesàro's Ω.
Mémoires de l'Académie de Belgique, 6 février 1886;Anncli, vol. 14, pp. 141 et seq.
Annali, loc. cit., p. 155, (12), (13).
Bulletin of the American Mathematical Society, Transactions (of the same) vol. 25, pp. 145–154.
Tohoku Mathematical Journal, vol. 17, pp. 221–231;Trans. American Math. Soc., loc. cit.
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Bell, E.T. Transformations of relations between numerical functions. Annali di Matematica 4, 1–6 (1927). https://doi.org/10.1007/BF02409982
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DOI: https://doi.org/10.1007/BF02409982