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Title

Farey series and the Riemann hypothesis

Authors 1, 2

Affiliations

  1. Department of Liberal Arts and Sciences, University of Kinki, Iizuka, Fukuoka 820, Japan
  2. Department of Mathematical Sciences, Faculty of Science, Kyushu University, Fukuoka 812, Japan

Bibliography

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  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.
  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.
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  6. M. N. Huxley, The distribution of Farey points, I , Acta Arith. 18 (1971), 281-287.
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  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).
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  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.
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  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.
Acta Arithmetica
1996/75/4
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Pages:
351-374
Main language of publication
English
Received
1995-08-22
Published
1996
Exact and natural sciences