On the zeros of approximations of the Ramanujan Ξ-function

被引:4
|
作者
Ki, Haseo [1 ]
机构
[1] Yonsei Univ, Dept Math, Seoul 120749, South Korea
来源
RAMANUJAN JOURNAL | 2008年 / 17卷 / 01期
关键词
Ramanujan zeta function; Riemann hypothesis; zeros of approximations of the Ramanujan Xi-function;
D O I
10.1007/s11139-007-9046-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The analogue of the Riemann hypothesis for the Ramanujan zeta function states that all zeros of the Ramanujan Xi-function have real zeros only. We study the zeros of approximations of the Ramanujan Xi-function.
引用
收藏
页码:123 / 143
页数:21
相关论文
共 50 条
  • [1] On the zeros of approximations of the Ramanujan Ξ-function
    Haseo Ki
    The Ramanujan Journal, 2008, 17 : 123 - 143
  • [2] A note on the zeros of approximations of the Ramanujan Ξ-function
    Chirre, Andres
    Castanon, Oswaldo Velasquez
    RAMANUJAN JOURNAL, 2022, 57 (01): : 389 - 400
  • [3] On a Ramanujan type entire function and its zeros
    Dai, Dan
    Ismail, Mourad E. H.
    Wang, Xiang-Sheng
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 485 (02)
  • [4] Zeros of Ramanujan Polynomials
    Murty, M. Ram
    Smyth, Chris
    Wang, Rob J.
    JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2011, 26 (01) : 107 - 125
  • [5] On the Zeros of Ramanujan Filters
    Kulkarni, Pranav
    Vaidyanathan, P. P.
    IEEE SIGNAL PROCESSING LETTERS, 2020, 27 : 735 - 739
  • [6] A Bernstein function related to Ramanujan’s approximations of exp(n)
    Stamatis Koumandos
    The Ramanujan Journal, 2013, 30 : 447 - 459
  • [7] A Bernstein function related to Ramanujan's approximations of exp(n)
    Koumandos, Stamatis
    RAMANUJAN JOURNAL, 2013, 30 (03): : 447 - 459
  • [8] Zeros of a Family of Approximations of the Riemann Zeta-Function
    Gonek, Steven M.
    Montgomery, Hugh L.
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2013, 2013 (20) : 4712 - 4733
  • [9] ALGEBRAIC APPROXIMATIONS TO THE LOCUS OF PARTITION-FUNCTION ZEROS
    WOOD, DW
    TURNBULL, RW
    BALL, JK
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1987, 20 (11): : 3495 - 3521
  • [10] Sharp Approximations for the Ramanujan Constant
    Song-Liang Qiu
    Xiao-Yan Ma
    Ti-Ren Huang
    Constructive Approximation, 2020, 51 : 303 - 330