Displaying similar documents to “Geometric properties of the zeta function”

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.

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.