On explicit estimates for \(S(t)\), \(S_1(t)\), and \(\zeta ( 1 / 2 + \operatorname{i} t )\) under the Riemann hypothesis

DOI10.1016/j.jnt.2021.05.014zbMath1489.11124arXiv2010.13307OpenAlexW3183791929WikidataQ114156934 ScholiaQ114156934MaRDI QIDQ2239166

Yanyan Li

Publication date: 3 November 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.13307

zbMATH Keywords

Riemann zeta-functionconditional explicit results

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (7)

The mean square of the error term in the prime number theorem ⋮ An explicit upper bound for \(|\zeta (1 + i t)|\) ⋮ On the Atkinson formula for the \(\zeta\) function ⋮ NEW EFFECTIVE RESULTS IN THE THEORY OF THE RIEMANN ZETA-FUNCTION ⋮ Estimates for \(L\)-functions in the critical strip under GRH with effective applications ⋮ An improved explicit estimate for \(\zeta(1/2 + it)\) ⋮ Conditional estimates for the logarithmic derivative of Dirichlet \(L\)-functions

Cites Work

• Unnamed Item
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• An explicit van der Corput estimate for \(\zeta(1/2+it)\)
• Improvements to Turing's method. II
• An improved explicit bound on \(| \zeta(\frac{1}{2} + i t) |\)
• On some theorems of Littlewood and Selberg. I
• Moments of the Riemann zeta function
• Lehmer pairs and derivatives of Hardy's \(Z\)-function
• Bandlimited approximations and estimates for the Riemann zeta-function
• Bounding \(S(t)\) and \(S_1(t)\) on the Riemann hypothesis
• Approximate formulas for some functions of prime numbers
• Decoupling, exponential sums and the Riemann zeta function
• Bounding |ζ(½+it )| on the Riemann hypothesis
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• Hyperbolic distance and distinct zeros of the Riemann zeta-function in small regions
• The explicit upper bound of the multiple integral of $S(t)$ on the Riemann Hypothesis
• Accurate estimation of sums over zeros of the Riemann zeta-function
• A note on S(t ) and the zeros of the Riemann zeta-function
• The argument of the Riemann zeta function

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