Farey series and the Riemann hypothesis
S. Kanemitsu ; M. Yoshimoto
Acta Arithmetica, Tome 76 (1996), p. 351-374 / Harvested from The Polish Digital Mathematics Library
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     title = {Farey series and the Riemann hypothesis},
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     volume = {76},
     year = {1996},
     pages = {351-374},
     zbl = {0860.11047},
     language = {en},
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S. Kanemitsu; M. Yoshimoto. Farey series and the Riemann hypothesis. Acta Arithmetica, Tome 76 (1996) pp. 351-374. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav75i4p351bwm/

[000] [1] P. Codecà, Alcune proprietà della discrepanza locale delle sequenze di Farey, Atti Accad. Sci. Istit. Bologna 13 (1981), 163-173.

[001] [2] P. Codecà and A. Perelli, On the uniform distribution (mod 1) of the Farey fractions and lp spaces, Math. Ann. 279 (1988), 413-422. | Zbl 0606.10041

[002] [3] J. Franel, Les suites de Farey et les problèmes des nombres premiers, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1924, 198-201.

[003] [4] A. Fujii, A remark on the Riemann hypothesis, Comment. Math. Univ. St. Paul. 29 (1980), 195-201. | Zbl 0451.10025

[004] [5] A. Fujii, Some explicit formulas in number theory, Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), 326-330. | Zbl 0492.10034

[005] [6] M. N. Huxley, The distribution of Farey points, I , Acta Arith. 18 (1971), 281-287. | Zbl 0224.10036

[006] [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. | Zbl 0601.10032

[007] [8] T. Kano, The Riemann Hypothesis, Nihonhyôronsha, 1990 (in Japanese).

[008] [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). | Zbl 0059.03801

[009] [10] J. Kopriva, Contribution to the relation of the Farey series to the Riemann hypothesis, Časopis Pěst. Mat. 79 (1954), 77-82 (in Czech). | Zbl 0059.03802

[010] [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. | Zbl 50.0119.02

[011] [12] E. Landau, Vorlesungen über Zahlentheorie, Teubner, 1927; Chelsea reprint, 1947.

[012] [13] L. Lewin, Polylogarithms and Associated Functions, North-Holland, 1981.

[013] [14] M. Mikolás, Farey series and their connection with the prime number problem I, Acta Sci. Math. (Szeged) 13 (1949), 93-117. | Zbl 0035.31402

[014] [15] M. Mikolás, Farey series and their connection with the prime number problem II, Acta Sci. Math. (Szeged) 14 (1951), 5-21. | Zbl 0042.27104

[015] [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. | Zbl 0758.11011

[016] [17] J. Milnor, On polylogarithms , Hurwitz zeta functions , and the Kubert identities, Enseign. Math. 29 (1983), 281-322. | Zbl 0557.10031

[017] [18] H. Niederreiter, The distribution of Farey points, Math. Ann. 201 (1973), 341-345. | Zbl 0248.10013

[018] [19] R. Sczech, Dedekindsummen mit elliptischen Funktionen, Invent. Math. 76 (1984), 523-551. | Zbl 0521.10021

[019] [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.

[020] [21] A. Zulauf, The distribution of Farey numbers, J. Reine Angew. Math. 289 (1977), 209-213. | Zbl 0336.10003