On the modulus of the Riemann zeta function in the critical strip

Filip Saidak; Peter D. Zvengrowski

Displaying similar documents to “On the modulus of the Riemann zeta function in the critical strip”

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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Small values of the Riemann zeta function on the critical line

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.

Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.

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.

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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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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A relation between the Riemann zeta-function and the hyperbolic laplacian

Yoichi Motohashi (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Geometric properties of the zeta function

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

Acta Arithmetica

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Bounds for double zeta-functions

Isao Kiuchi, Yoshio Tanigawa (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region $0 \leq ℜ s_{j} < 1 (j = 1, 2)$ .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.