Department of Mathematical Sciences, Faculty of Science, Kyushu University, Fukuoka 812, Japan
Bibliografia
[1] P. Codecà, Alcune proprietà della discrepanza locale delle sequenze di Farey, Atti Accad. Sci. Istit. Bologna 13 (1981), 163-173.
[2] P. Codecà and A. Perelli, On the uniform distribution (mod 1) of the Farey fractions and $l^p$ spaces, Math. Ann. 279 (1988), 413-422.
[3] J. Franel, Les suites de Farey et les problèmes des nombres premiers, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1924, 198-201.
[4] A. Fujii, A remark on the Riemann hypothesis, Comment. Math. Univ. St. Paul. 29 (1980), 195-201.
[5] A. Fujii, Some explicit formulas in number theory, Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), 326-330.
[6] M. N. Huxley, The distribution of Farey points, I , Acta Arith. 18 (1971), 281-287.
[7] M. Ishibashi and S. Kanemitsu, Fractional part sums and divisor functions I, in: Number Theory and Combinatorics, J. Akiyama et al . (eds.), World Sci., 1985, 119-193.
[8] T. Kano, The Riemann Hypothesis, Nihonhyôronsha, 1990 (in Japanese).
[9] J. Kopriva, On a relation of the Farey series to the Riemann hypothesis on the zeros of the ζ function, Časopis Pěst. Mat. 78 (1953), 49-55 (in Czech).
[10] J. Kopriva, Contribution to the relation of the Farey series to the Riemann hypothesis, Časopis Pěst. Mat. 79 (1954), 77-82 (in Czech).
[11] E. Landau, Bemerkungen zu vorstehenden Abhandlung von Herrn Franel, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1924, 202-206; Collected Works, Vol. 8, Thales Verlag.
[12] E. Landau, Vorlesungen über Zahlentheorie, Teubner, 1927; Chelsea reprint, 1947.
[13] L. Lewin, Polylogarithms and Associated Functions, North-Holland, 1981.
[14] M. Mikolás, Farey series and their connection with the prime number problem I, Acta Sci. Math. (Szeged) 13 (1949), 93-117.
[15] M. Mikolás, Farey series and their connection with the prime number problem II, Acta Sci. Math. (Szeged) 14 (1951), 5-21.
[16] M. Mikolás and K.-I. Sato, On the asymptotic behaviour of Franel's sum and the Riemann hypothesis, Results Math. 21 (1992), 368-378.
[17] J. Milnor, On polylogarithms , Hurwitz zeta functions , and the Kubert identities, Enseign. Math. 29 (1983), 281-322.
[18] H. Niederreiter, The distribution of Farey points, Math. Ann. 201 (1973), 341-345.
[19] R. Sczech, Dedekindsummen mit elliptischen Funktionen, Invent. Math. 76 (1984), 523-551.
[20] Y. Yamamoto, Dirichlet series with periodic coefficients, in: Proc. Intern. Sympos. Algebraic Number Theory, Kyoto 1976, Japan Society for the Promotion of Science, 1977, 275-289.
[21] A. Zulauf, The distribution of Farey numbers, J. Reine Angew. Math. 289 (1977), 209-213.
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Bibliografia
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