The Riemann hypothesis is true up to 3·1012
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Publication:5006390
DOI10.1112/blms.12460zbMath1482.11111arXiv2004.09765OpenAlexW3121963155MaRDI QIDQ5006390
Publication date: 13 August 2021
Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.09765
(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)
Related Items (26)
Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function ⋮ The sum of divisors function and the Riemann hypothesis ⋮ Robin's inequality for 20-free integers ⋮ Explicit interval estimates for prime numbers ⋮ Counting zeros of the Riemann zeta function ⋮ On primes, almost primes, and the Möbius function in short intervals ⋮ The Selberg-Delange method and mean value of arithmetic functions over short intervals ⋮ Sharper bounds for the error term in the prime number theorem ⋮ On the error term in the explicit formula of Riemann–von Mangoldt ⋮ Sharper bounds for the Chebyshev function \(\psi(x)\) ⋮ Some explicit estimates for the error term in the prime number theorem ⋮ New bounds for numbers of primes in element orders of finite groups ⋮ Calculation of the values of the Riemann zeta function via values of its derivatives at a single point ⋮ Explicit zero-free regions for the Riemann zeta-function ⋮ Scalar modular bootstrap and zeros of the Riemann zeta function ⋮ Towards non-iterative calculation of the zeros of the Riemann zeta function ⋮ Corrigendum to ‘Explicit interval estimates for prime numbers’ ⋮ A computational approach to the generalized Riemann hypothesis ⋮ Explicit bounds on \(\zeta (s)\) in the critical strip and a zero-free region ⋮ The Laguerre-Pólya class and combinatorics. Abstracts from the workshop held March 13--19, 2022 ⋮ A note on the zeros of Jensen polynomials ⋮ Primes between consecutive powers ⋮ Sign changes in the prime number theorem ⋮ Jensen polynomials for the Riemann xi-function ⋮ Improving bounds on prime counting functions by partial verification of the Riemann hypothesis ⋮ New results for witnesses of Robin’s criterion
Cites Work
- Improvements to Turing's method. II
- An improved explicit bound on \(| \zeta(\frac{1}{2} + i t) |\)
- Explicit bounds for primes in arithmetic progressions
- Explicit zero density for the Riemann zeta function
- Explicit estimates of some functions over primes
- Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function
- Explicit zero density estimate for the Riemann zeta-function near the critical line
- Effective approximation of heat flow evolution of the Riemann \(\xi \) function, and a new upper bound for the de Bruijn-Newman constant
- An improved upper bound for the argument of the Riemann zeta-function on the critical line. II
- Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function
- Approximate formulas for some functions of prime numbers
- On the first sign change of $\theta (x) -x$
- Estimating $\pi (x)$ and related functions under partial RH assumptions
- A zero density result for the Riemann zeta function
- Every odd number greater than $1$ is the sum of at most five primes
- Isolating some non-trivial zeros of zeta
- Improvements to Turing’s method
- Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
- Zero-free regions for the Riemann zeta function
- Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic
- Corrigendum to New bounds for $\psi (x)$
- An analytic method for bounding 𝜓(𝑥)
- Explicit estimates for the summatory function of \varLambda (n)ń from the one of \varLambda (n)
- THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE
- The error term in the prime number theorem
- Short effective intervals containing primes
- A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive
- A practical analytic method for calculating $\pi (x)$
- The ternary Goldbach problem
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