Farey series and the riemann hypothesis III

被引：0
|
作者：
Kanemitsu S. [1 ]
Yoshimoto M. [2 ]
机构：
[1] Department of Liberal Arts and Sciences, University of Kinki, Iizuka
[2] Graduate School of Mathematics, Kyushu University
来源：
The Ramanujan Journal | 1997年 / 1卷 / 4期
关键词：
Dirichlet character; Farey series; Riemann hypothesis;
D O I：
10.1023/A:1009705826419
中图分类号：
学科分类号：
摘要：
In this paper we shall make a further study on the "the equivalence problem," i.e., equivalent conditions to the Riemann hypothesis in terms of Farey series by developing a rather analytical (-arithmetical) method to establish unexpected short interval results, namely 1/5-, 1/6- results, therewith simultaneously clarifying the underlying reasons for 1/2-, 1/3-, 1/4- results obtained in Part I. © 1997 Kluwer Academic Publishers.
引用
收藏
页码：363 / 378
页数：15
相关论文
共 50 条
  • [1] Farey series and the Riemann hypothesis
    Kanemitsu, S
    Yoshimoto, M
    ACTA ARITHMETICA, 1996, 75 (04) : 351 - 374
  • [2] Abelian theorems, Farey series and the Riemann hypothesis
    Yoshimoto, M
    RAMANUJAN JOURNAL, 2004, 8 (02): : 131 - 145
  • [3] Farey Series and the Riemann Hypothesis. IV
    M. Yoshimoto
    Acta Mathematica Hungarica, 2000, 87 : 109 - 119
  • [4] Euler products, Farey series and the Riemann hypothesis
    Kanemitsu, S
    Yoshimoto, M
    PUBLICATIONES MATHEMATICAE DEBRECEN, 2000, 56 (3-4): : 431 - 449
  • [5] Abelian Theorems, Farey Series and the Riemann Hypothesis
    Masami Yoshimoto
    The Ramanujan Journal, 2004, 8 : 131 - 145
  • [6] Farey series and the Riemann hypothesis. II
    Yoshimoto, M
    ACTA MATHEMATICA HUNGARICA, 1998, 78 (04) : 287 - 304
  • [7] Farey Series and the Riemann Hypothesis. II
    M. Yoshimoto
    Acta Mathematica Hungarica, 1998, 78 : 287 - 304
  • [8] Farey series and the Riemann hypothesis. IV
    Yoshimoto, M
    ACTA MATHEMATICA HUNGARICA, 2000, 87 (1-2) : 109 - 119
  • [9] Euler products, Farey series, and the Riemann hypothesis II
    Balasubramanian, R.
    Kanemitsu, S.
    Yoshimoto, M.
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2006, 69 (1-2): : 1 - 16
  • [10] A note on series equivalent of the Riemann hypothesis
    Suman, Shekhar
    Das, Raman Kumar
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, 54 (01): : 117 - 119
12345