Bounding $\zeta (s)$ in the critical strip

Abstract

Assuming the Riemann Hypothesis, we make use of the recently discovered \cite{CLV} extremal majorants and minorants of prescribed exponential type for the function $\log \left(\frac{4+x^2}{(\alpha -1/2{)}^2+x^2}\right)$ to find upper and lower bounds with explicit constants for $\log |\zeta (\alpha +it)|$ in the critical strip, extending the work of Chandee and Soundararajan \cite{CS}.

References in corpus (4)

• Gaussian Subordination for the Beurling-Selberg Extremal Problem
• Some extremal functions in Fourier analysis, II
• A note on S(T) and the zeros of the Riemann zeta-function
• Explicit Upper Bounds for L-functions on the critical line

Cited by in corpus (17)

• Gaussian Subordination for the Beurling-Selberg Extremal Problem
• Bounding $S(t)$ and $S_1(t)$ on the Riemann hypothesis
• Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function
• Extremal functions in de Branges and Euclidean spaces
• Bandlimited approximations to the truncated Gaussian and applications
• The angle of large values of $L$-functions
• Traces, high powers and one level density for families of curves over finite fields
• On the argument of $L$-functions
• Bounding $S_n(t)$ on the Riemann hypothesis
• The mean values of cubic L-functions over function fields
• Extremal problems in de Branges spaces: the case of truncated and odd functions
• Extremal functions in de Branges and Euclidean spaces II
• Entire approximations for a class of truncated and odd functions
• Extreme values of derivatives of zeta and $L$-functions
• A Variation on Selberg's Approximation Problem
• The Ratios Conjecture and upper bounds for negative moments of $L$-functions over function fields
• Mean value of real characters using a double Dirichlet series