Displaying similar documents to “A sequential Riesz-like criterion for the Riemann Hypothesis.”

Small values of the Riemann zeta function on the critical line

Justas Kalpokas, Paulius Šarka (2015)

Acta Arithmetica

Similarity:

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 zero density result for the Riemann zeta function

Habiba Kadiri (2013)

Acta Arithmetica

Similarity:

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.

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

Maxim A. Korolev (2014)

Acta Arithmetica

Similarity:

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 family of deformations of the Riemann xi-function

Masatoshi Suzuki (2013)

Acta Arithmetica

Similarity:

We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.