The Riemann Zeta function and coin tossing.
P.D.T.A. Elliott (1972)
Journal für die reine und angewandte Mathematik
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P.D.T.A. Elliott (1972)
Journal für die reine und angewandte Mathematik
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Akio Fujii (1979)
Journal für die reine und angewandte Mathematik
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D.A. Goldston (1988)
Journal für die reine und angewandte Mathematik
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Akio Fujii (1978)
Journal für die reine und angewandte Mathematik
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J.B. Conrey (1989)
Journal für die reine und angewandte Mathematik
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J. Kaczorowski, A. Perelli (2005)
Acta Arithmetica
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P.X. Gallagher (1985)
Journal für die reine und angewandte Mathematik
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Aleksandar Ivić (1989)
Publications de l'Institut Mathématique
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Norman Levinson (1972)
Acta Arithmetica
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Yu. Matiyasevich, F. Saidak, P. Zvengrowski (2014)
Acta Arithmetica
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As usual, let s = σ + it. For any fixed value of t with |t| ≥ 8 and for σ < 0, we show that |ζ(s)| is strictly decreasing in σ, with the same result also holding for the related functions ξ of Riemann and η of Euler. The following inequality related to the monotonicity of all three functions is proved: ℜ (η'(s)/η(s)) < ℜ (ζ'(s)/ζ(s)) < ℜ (ξ'(s)/ξ(s)). It is also shown that extending the above monotonicity result for |ζ(s)|, |ξ(s)|, or |η(s)|...
A. Laurinčikas (1990)
Acta Arithmetica
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Masanori Katsurada (2003)
Acta Arithmetica
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Habiba Kadiri (2013)
Acta Arithmetica
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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
Kazufumi Kimoto, Nobushige Kurokawa, Sho Matsumoto, Masato Wakayama (2005)
Acta Arithmetica
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