7 citations · 13 across the 6 of their papers we have counts for
6 papers
Average prime-pair counting formula
Jaap Korevaar, Herman te Riele
Taking , let denote the number of prime pairs with . The prime-pair conjecture of Hardy and Littlewood (1923) asserts that $π_{2r}(x)\sim 2C_{2…
Ikehara-type theorem involving boundedness
Jacob Korevaar
Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s…
Lower bound for the remainder in the prime-pair conjecture
Jacob Korevaar
For any positive integer r, let pi_{2r}(x) denote the number of prime pairs (p, p+2r) with p not exceeding (large) x. According to the prime-pair conjecture of Hardy and Littlewood…
Mean value one of prime-pair constants
Fokko van de Bult, Jaap Korevaar
For k greater than 1 and r different from 0, let pi^k_{2r}(x) denote the number of prime pairs (p,p^k+2r) with p not exceeding (large) x. By the Bateman-Horn conjecture, the functi…
Prime pairs and Zeta's zeros
Jacob Korevaar
There is extensive numerical support for the prime-pair conjecture (PPC) of Hardy and Littlewood (1923) on the asymptotic behavior of pi_{2r}(x), the number of prime pairs (p,p+2r)…
A Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior
Jaap Korevaar
The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consid…