New estimates for some functions defined over primes

zbMath1440.11184arXiv1703.08032MaRDI QIDQ5384263

Christian Axler

Publication date: 21 June 2019

Full work available at URL: https://arxiv.org/abs/1703.08032

zbMATH Keywords

prime counting functionChebyshev's \(\vartheta\)-function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution of primes (11N05) Primes (11A41)

Related Items (12)

Explicit interval estimates for prime numbers ⋮ Unnamed Item ⋮ New estimates for some integrals of functions defined over primes ⋮ Some explicit estimates for the error term in the prime number theorem ⋮ ON THE ITERATES OF THE SHIFTED EULER’S FUNCTION ⋮ On the sum of the first \(n\) prime numbers ⋮ On the constant factor in several related asymptotic estimates ⋮ New estimates for the $n$th prime number ⋮ The constant factor in the asymptotic for practical numbers ⋮ Sharper bounds for the Chebyshev function 𝜃(𝑥) ⋮ AN ARITHMETIC EQUIVALENCE OF THE RIEMANN HYPOTHESIS ⋮ Variants on Andrica's conjecture with and without the Riemann hypothesis

Uses Software

• OEIS

Cites Work

• On a constant related to the prime counting function
• Explicit estimates of some functions over primes
• An explicit result for primes between cubes
• Short effective intervals containing primes
• 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
• Estimates of $\psi ,\theta $ for large values of $x$ without the Riemann hypothesis
• Estimating $\pi (x)$ and related functions under partial RH assumptions
• New bounds for the prime counting function \pi(x)
• An explicit density estimate for Dirichlet $L$-series
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• An analytic method for bounding 𝜓(𝑥)
• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• Short effective intervals containing primes
• Une région explicite sans zéros pour la fonction ζ de Riemann
• Updating the error term in the prime number theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: New estimates for some functions defined over primes