Small values of the Riemann zeta function on the critical line

Justas Kalpokas; Paulius Šarka

Displaying similar documents to “Small values of the Riemann zeta function on the critical line”

On large values of the Riemann zeta-function on short segments of the critical line

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 note on the zeros of the derivative of the Riemann zeta function near the critical line

Shaoji Feng (2005)

Acta Arithmetica

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Note on a paper by H. L. Montgomery (Omega theorems for the Riemann zeta- function).

Ramachandra, K., Sankaranarayanan, A. (1991)

Publications de l'Institut Mathématique. Nouvelle Série

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Geometric properties of the zeta function

Hugh L. Montgomery, John G. Thompson (2012)

Acta Arithmetica

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On the error term of the mean square formula for the Riemann zeta-function in the critical strip 3/4 < σ < 1

Yuk-Kam Lau (2002)

Acta Arithmetica

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A limit theorem for the Riemann zeta-function in the complex space

A. Laurinčikas (1990)

Acta Arithmetica

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Ω-theorems for the Riemann zeta-function

Norman Levinson (1972)

Acta Arithmetica

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Zeros of the Riemann Zeta-function on the critical line.

D.R. Heath-Brown (1993)

Mathematische Zeitschrift

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On the Mean Square Formula for the Riemann Zeta-Function on the Critical Line.

Yuk-Kam Lau (1994)

Monatshefte für Mathematik

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More than 41% of the zeros of the zeta function are on the critical line

H. M. Bui, Brian Conrey, Matthew P. Young (2011)

Acta Arithmetica

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Borwein and Bradley's Apéry-like formulae for $ζ (4 n + 3)$ .

Almkvist, Gert, Granville, Andrew (1999)

Experimental Mathematics

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On the Fourth Moment of the Riemann Zeta Functions

Aleksandar Ivić (1995)

Publications de l'Institut Mathématique

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On the success and failure of Gram's Law and the Rosser Rule

Timothy Trudgian (2011)

Acta Arithmetica

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A zero density result for the Riemann zeta function

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.