The k-functions in multiplicative number theory. III. Uniform distribution of zeta zeros; discrepancy
J. Kaczorowski (1991)
Acta Arithmetica
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J. Kaczorowski (1991)
Acta Arithmetica
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J. Kaczorowski, A. Perelli (2008)
Acta Arithmetica
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Csordas, George, Yang, Chung-Chun (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Tsz Ho Chan (2004)
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.
James Haglund (2011)
Open Mathematics
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Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show...
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.
Ming-Chit Liu, Tianze Wang (2002)
Acta Arithmetica
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D.A. Goldston (1988)
Journal für die reine und angewandte Mathematik
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Sarnak, Peter (1998)
Documenta Mathematica
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D. Heath-Brown (1982)
Acta Arithmetica
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Yuichi Kamiya, Masatoshi Suzuki (2004)
Publications de l'Institut Mathématique
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Farmer, David W. (1995)
The Electronic Journal of Combinatorics [electronic only]
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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.