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Item type:Publication, Conditional Estimates for the Logarithmic Derivative of Dirichlet L-Functions(Elsevier BV, 2023-07-31)Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the q-aspect for the logarithmic derivative L′/Lσ,χ of Dirichlet L-functions, where χ is a primitive character modulo q≥1030 and 1/2+1/loglogq≤σ≤1−1/loglogq. In addition, for σ=1 we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Explicit conditional bounds for $\zeta(s)$ at the edge of the critical strip(European Mathematical Society, 2026-06-19)In this paper, we obtain explicit bounds for the real part of the logarithmic derivative of the Riemann zeta-function on the line \operatorname{Re}s=1 , assuming the Riemann hypothesis. The proof combines the Guinand–Weil explicit formula with extremal bandlimited majorants and minorants for the Poisson kernel. As an application, we revisit the classical estimates of Littlewood for the modulus of the Riemann zeta-function and of its reciprocal on the line \operatorname{Re}{s}=1 , and derive a slight refinement of the bounds of Lamzouri, Li, and Soundararajan. In addition, we establish an explicit bound for the modulus of the logarithmic derivative of the Riemann zeta-function on the line \operatorname{Re}{s}=1 under the Riemann hypothesis, improving the lower-order term in a result of Chirre, Hagen, and Simonič.