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

Maxim A. Korolev

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Small values of the Riemann zeta function on the critical line

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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.

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

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A zero density result for the Riemann zeta function

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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.