Zeros of the Riemann Zeta-function on the critical line.
D.R. Heath-Brown (1993)
Mathematische Zeitschrift
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D.R. Heath-Brown (1993)
Mathematische Zeitschrift
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H. M. Bui, Brian Conrey, Matthew P. Young (2011)
Acta Arithmetica
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Timothy Trudgian (2011)
Acta Arithmetica
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Shaoji Feng (2005)
Acta Arithmetica
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Justas Kalpokas, Paulius Šarka (2015)
Acta Arithmetica
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We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.
J.B. Conrey (1989)
Journal für die reine und angewandte Mathematik
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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.
Laurinčikas, Antanas, Steuding, Jörn (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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S. Chowla (1934)
Mathematische Zeitschrift
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Maxim A. Korolev (2014)
Acta Arithmetica
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We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.
A. Ivic, M. Jutila (1988)
Monatshefte für Mathematik
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Yuk-Kam Lau (1994)
Monatshefte für Mathematik
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Ramachandra, K., Sankaranarayanan, A. (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Daniel Bump, Eugene K.-S. Ng (1986)
Mathematische Zeitschrift
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