Farey series and the Riemann hypothesis

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1. [1] P. Codecà, Alcune proprietà della discrepanza locale delle sequenze di Farey, Atti Accad. Sci. Istit. Bologna 13 (1981), 163-173. 
2. [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. Zbl0606.10041
3. [3] J. Franel, Les suites de Farey et les problèmes des nombres premiers, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1924, 198-201. 
4. [4] A. Fujii, A remark on the Riemann hypothesis, Comment. Math. Univ. St. Paul. 29 (1980), 195-201. Zbl0451.10025
5. [5] A. Fujii, Some explicit formulas in number theory, Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), 326-330. Zbl0492.10034
6. [6] M. N. Huxley, The distribution of Farey points, I , Acta Arith. 18 (1971), 281-287. Zbl0224.10036
7. [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. Zbl0601.10032
8. [8] T. Kano, The Riemann Hypothesis, Nihonhyôronsha, 1990 (in Japanese). 
9. [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). Zbl0059.03801
10. [10] J. Kopriva, Contribution to the relation of the Farey series to the Riemann hypothesis, Časopis Pěst. Mat. 79 (1954), 77-82 (in Czech). Zbl0059.03802
11. [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. Zbl50.0119.02
12. [12] E. Landau, Vorlesungen über Zahlentheorie, Teubner, 1927; Chelsea reprint, 1947. 
13. [13] L. Lewin, Polylogarithms and Associated Functions, North-Holland, 1981. 
14. [14] M. Mikolás, Farey series and their connection with the prime number problem I, Acta Sci. Math. (Szeged) 13 (1949), 93-117. Zbl0035.31402
15. [15] M. Mikolás, Farey series and their connection with the prime number problem II, Acta Sci. Math. (Szeged) 14 (1951), 5-21. Zbl0042.27104
16. [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. Zbl0758.11011
17. [17] J. Milnor, On polylogarithms , Hurwitz zeta functions , and the Kubert identities, Enseign. Math. 29 (1983), 281-322. Zbl0557.10031
18. [18] H. Niederreiter, The distribution of Farey points, Math. Ann. 201 (1973), 341-345. Zbl0248.10013
19. [19] R. Sczech, Dedekindsummen mit elliptischen Funktionen, Invent. Math. 76 (1984), 523-551. Zbl0521.10021
20. [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. [21] A. Zulauf, The distribution of Farey numbers, J. Reine Angew. Math. 289 (1977), 209-213. Zbl0336.10003