Quelques références sur la distribution de la suite de Farey

par

Francesco AMOROSO

 

Amoroso, F.
``On the heights of a product of cyclotomic polynomials."
Number theory, I (Rome, 1995). Rend. Sem. Mat. Univ. Politec. Torino
53 (1995), no. 3, 183--191.

Amoroso, F.
``Algebraic numbers close to 1 and variants of Mahler's measure."
J. Number Theory
60 (1996), no. 1, 80--96.

Codecà, P.
``Some properties of the local discrepancy of Farey sequences."
Atti Accad. Sci. Istit. Bologna Cl. Sci. Fis. Rend (13)
8 (1980/81), no. 1-2, 163-173.

Codecà, P. and Perelli, A.
``On the uniform distribution (mod 1) of the Farey fractions and l^p spaces."
Math. Ann.
279 (1988), no. 3, 413-422.

Franel, J.
``Les suites de Farey et les problèmes des nombres premiers."
Göttinger Nachrichten, 198-201 (1924).

Fujii, A.
``A remark on the Riemann hypothesis."
Comment. Math. Univ. St. Pauli
29 (1980), 195-201 .

Fujii, A.
``Some explicit formulae in the theory of numbers. A remark on the Riemann Hypothesis."
Proc. Japan Acad., Ser. A
57 (1981), 326-330 .

Huxley, M.N.
``The distribution of Farey points, I."
Acta Arith.
18 (1971), 281-287 .

Kanemitsu, S. and Yoshimoto, M.
``Farey series and the Riemann hypothesis."
Acta Arith.
75 (1996), no. 4, 351-374.

Kanemitsu, S. and Yoshimoto, M.
``Farey series and the Riemann hypothesis. III."
Ramanujan J.
1 (1997), no. 4, 363-378 .

Kopriva, J.
``Contribution to the relation of the Farey series to the Riemann hypothesis on the zeros of the zeta function"
(Czech), Casopis Pêst. Mat.
78 (1953), 49-55 .

Kopriva, J.
``Contribution to the relation of the Farey series to the Riemann hypothesis"
(Czech), Casopis Pêst. Mat.
79 (1954), 77-82 .

Landau, E.
``Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel."
Göttinger Nachrichten, 202-206 (1924);.

Mikolàs, M.
``Sur l'hypothèse de Riemann."
C. R. Acad. Sci. Paris
228 (1949), 633-636.

Mikolàs, M.
``Farey series and their connection with the prime number problem. I."
Acta Univ. Szeged. Sect. Sci. Math.
13 (1949), 93-117.

Mikolàs, M.
``Farey series and their connection with the prime number problem. II."
Acta Univ. Szeged. Sect. Sci. Math.
14 (1951), 5-21.

Mikolàs, M.
``On the asymptotic behaviour of Franel's sum and the Riemann hypothesis."
Results Math
21 (1992), no. 3--4, 368-378.

Niederreiter, E.
``The distribution of Farey points",
Math. Ann. 201 (1973), 341-345.

Yoshimoto, M.
``Farey series and the Riemann hypothesis. II."
Acta Math. Hungar.
78 (1998), no. 4, 287-304.

Zulauf, A.
``The distribution of Farey Numbers."
J. Reine Angew. Math.
289 (1977), 209-213.


Francesco AMOROSO
Département de Mathématiques
Université de Caen
Campus II, BP 5186
14032 Caen Cedex
France
 
e-mail: amoroso@math.unicaen.fr

Mise à jour: 7 Décembre 1999

URL : http://www.math.jussieu.fr/~miw/telecom/biblio-Amoroso.html

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