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Item type:Publication, An extremal problem and inequalities for entire functions of exponential type(American Mathematical Society, 2024-08-01)We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath eodory-Fej er- Turán problem. The first variation imposes the additional requirement that the function is radially decreasing while the second one is a generalization which involves derivatives of the entire function. Various interesting inequalities, inspired by results due to Duffin and Schaeffer, Landau, and Hardy and Littlewood, are also established. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Bounding zeta on the 1-line under the partial Riemann hypothesis(Cambridge University Press, 2024-10-01)We provide explicit bounds for the Riemann zeta-function on the line, assuming that the Riemann hypothesis holds up to height T. In particular, we improve some bounds in finite regions for the logarithmic derivative and the reciprocal of the Riemann zeta-function. - Some of the metrics are blocked by yourconsent settings
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, Optimal bounds for sums of bounded arithmetic functions(Centre National de la Recherche Scientifique, 2025-11-19)1 - 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. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Explicit conditional bounds for $ζ(s)$ at the edge of the critical strip(Cornell University, 2026-02-05)In this paper, we obtain explicit bounds for the real part of the logarithmic derivative of the Riemann zeta-function on the line $\re s=1$, 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 $\re{s}=1$, 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 $\re{s}=1$ under the Riemann hypothesis, improving the lower-order term in a result of Chirre, Valås, and Simonič.1