Caractérisation des fonctions multiplicatives presque-B λ périodiques à spectre non vide
Annales de l'Institut Fourier, Tome 30 (1980) no. 3, pp. 141-166.

Nous caractérisons, dans cet article, les fonctions multiplicatives presque périodiques au sens de Bésicovith ayant un spectre de Fourier non vide.

We give a characterization of multiplicative functions which are almost periodic in the sense of Bésicovitch and have a non empty Fourier spectrum.

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     author = {Daboussi, H\'edi},
     title = {Caract\'erisation des fonctions multiplicatives presque-$B^\lambda $ p\'eriodiques \`a spectre non vide},
     journal = {Annales de l'Institut Fourier},
     pages = {141--166},
     publisher = {Institut Fourier},
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     volume = {30},
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     year = {1980},
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Daboussi, Hédi. Caractérisation des fonctions multiplicatives presque-$B^\lambda $ périodiques à spectre non vide. Annales de l'Institut Fourier, Tome 30 (1980) no. 3, pp. 141-166. doi : 10.5802/aif.796. http://archive.numdam.org/articles/10.5802/aif.796/

[1] A.S. Besicovitch, Almost periodic functions, Dover Publications. | Zbl

[2] H. Daboussi et H. Delange, Quelques propriétés de fonctions multiplicatives, C.R. Acad. Sc., Paris, 278 Série A (1974), 657-660. | MR | Zbl

[3] H. Delange, Quelques résultats sur les fonctions multiplicatives, C.R. Acad. Sc., Paris, 281 Série A (1975), 997-1000. | MR | Zbl

[4] P.D.T.A. Elliott, On connections between the Turan-Kubilius inequality..., Proc. Symposia Math., Vol. XXIV, 77-82. | Zbl

[5] P.D.T.A. Elliott, A mean value theorem for multiplicative functions, Proc. London Math. Soc., (3), 31 (1975), 418-438. | MR | Zbl

[6] P. Erdös, Some remarks about additive and multiplicative functions, Bull. Am. Math. Soc., 52 (1946), 527-537 et Some remarks and corrections..., Bull. Am. Math. Soc., 53 (1947), 761-763. | Zbl

[7] P. Erdös and A. Renyi, On the mean value of non negative multiplicative..., Michigan Math. J., 12 (1965), 321-328. | Zbl

[8] P. Erdos and A. Wintner, Additive functions and almost periodicity B2, Amer. J. Math., 62 (1940), 635-645. | JFM | MR | Zbl

[9] P. Hartman and A. Wintner, On the almost periodicity of additive number..., Amer. J. Math., 62 (1940), 753-758. | JFM | MR | Zbl

[10] M. Kac, E.R. Van Kampen and A. Wintner, Ramanujan sums and almost periodic functions, Amer. J. Math., 62 (1940), 107-144. | JFM | MR | Zbl

[11] I. Kubilius, Probabilistic methods in the theory of numbers, Transl. Math. Monographs, vol. 11, Amer. Math. Soc. Providence.

[12] E.V. Novoselov, A new method in probabilistic number theory, Amer. Math. Soc. Transl., 52 (1966), 217-275. | Zbl

[13] W. Schwarz and J. Spilker, Mean values and Ramanujan expansions of almost E.A.C., Colloquia Math. S. Janos Bolyai 13, Topics in Number theory, Debrecen, 1974. | Zbl

[14] E.R. Van Kampen and A. Wintner, On the almost periodic behavior of multiplicative..., Amer. J. Math., 62 (1940), 613-626. | JFM | MR | Zbl

[15] A. Wintner, Number theoretical almost periodicities, Amer. J. Math., 67 (1945), 173-193. | MR | Zbl

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