On an Effective Order Estimate of the Riemann Zeta Function in the Critical Strip.
K.M. Bartz (1990)
Monatshefte für Mathematik
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K.M. Bartz (1990)
Monatshefte für Mathematik
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Aleksandar Ivic, K. Matsumoto (1996)
Monatshefte für Mathematik
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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.
A. Ivic, M. Jutila (1988)
Monatshefte für Mathematik
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Shaoji Feng (2005)
Acta Arithmetica
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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.
Yuk-Kam Lau (2002)
Acta Arithmetica
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Hugh L. Montgomery, John G. Thompson (2012)
Acta Arithmetica
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Ramachandra, K., Sankaranarayanan, A. (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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J.B. Conrey (1989)
Journal für die reine und angewandte Mathematik
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H. M. Bui, Brian Conrey, Matthew P. Young (2011)
Acta Arithmetica
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D.R. Heath-Brown (1993)
Mathematische Zeitschrift
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Timothy Trudgian (2011)
Acta Arithmetica
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Aleksandar Ivić (1989)
Publications de l'Institut Mathématique
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