Distributional Wiener-Ikehara theorem and twin primes

DOI10.1016/S0019-3577(05)80013-8zbMath1111.40005MaRDI QIDQ555946

Jacob Korevaar

Publication date: 10 June 2005

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

Laplace transformdistributionsTauberian theoremspseudofunctions

Mathematics Subject Classification ID

Laplace transform (44A10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Distribution of primes (11N05) Distributions and ultradistributions as boundary values of analytic functions (46F20) Tauberian theorems (40E05)

Related Items (17)

Optimal Tauberian constant in Ingham's theorem for Laplace transforms ⋮ A Tauberian theorem of Wiener-Ikehara type and its applications ⋮ On PNT equivalences for Beurling numbers ⋮ Charting the \(q\)-Askey scheme. II. The \(q\)-Zhedanov scheme ⋮ An Operator Theoretic Approach to the Prime Number Theorem ⋮ The prime-pair conjectures of Hardy and Littlewood ⋮ Local properties of Hilbert spaces of Dirichlet series ⋮ A generalization of the Banach-Steinhaus theorem for finite part limits ⋮ Average prime-pair counting formula ⋮ Tauberian class estimates for vector-valued distributions ⋮ Modified zeta functions as kernels of integral operators ⋮ Note on the absence of remainders in the Wiener-Ikehara theorem ⋮ On Diamond's \(L^1\) criterion for asymptotic density of Beurling generalized integers ⋮ The Wiener–Ikehara theorem by complex analysis ⋮ Prime pairs and the zeta function ⋮ On Wiener’s Tauberian theorems and convolution for oscillatory integral operators ⋮ Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Newman's quick way to the prime number theorem
• On Euler numbers, Hilbert sums, Lobachevskiǐ integrals, and their asymptotics
• A century of complex Tauberian theory
• The Wiener–Ikehara theorem by complex analysis
• Simple Analytic Proof of the Prime Number Theorem
• Newman's Short Proof of the Prime Number Theorem
• On the twin-prime problem, II

This page was built for publication: Distributional Wiener-Ikehara theorem and twin primes