The k-functions in multiplicative number theory. IV. On a method of A. E. Ingham
J. Kaczorowski (1991)
Acta Arithmetica
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J. Kaczorowski (1991)
Acta Arithmetica
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H. M. Bui (2014)
Acta Arithmetica
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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.
Yuichi Kamiya, Masatoshi Suzuki (2004)
Publications de l'Institut Mathématique
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Tsz Ho Chan (2004)
Acta Arithmetica
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D. Heath-Brown (1982)
Acta Arithmetica
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Akio Fujii (1978)
Journal für die reine und angewandte Mathematik
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Tsz Ho Chan (2004)
Acta Arithmetica
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Masatoshi Suzuki (2015)
Acta Arithmetica
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We show that the density functions of nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines are described by the M-function which appears in value distribution of the logarithmic derivative of the Riemann zeta-function on vertical lines.
D.A. Goldston (1988)
Journal für die reine und angewandte Mathematik
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J. Kaczorowski, A. Perelli (2008)
Acta Arithmetica
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Riad Masri (2007)
Acta Arithmetica
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Laurinčikas, Antanas, Steuding, Jörn (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Juan Arias de Reyna, Jan van de Lune (2014)
Acta Arithmetica
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We introduce the real valued real analytic function κ(t) implicitly defined by (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ’(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.
Csordas, George, Yang, Chung-Chun (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Farmer, David W. (1995)
The Electronic Journal of Combinatorics [electronic only]
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