Learn More
Complex-analytic and related boundary properties of transforms give information on the behavior of pre-images. The transforms may be power series, Dirichlet series or Laplace-type integrals; the pre-images are series (of numbers) or functions. The chief impulse for complex Tauberian theory came from number theory. The first part of the survey emphasizes(More)
For k > 1, r = 0 and large x, let π k 2r (x) denote the number of prime pairs (p, p k + 2r) with p ≤ x. By the Bateman–Horn conjecture the function π k 2r (x) should be asymptotic to (2/k)C k 2r li 2 (x), with certain specific constants C k 2r. Heuristic arguments lead to the conjecture that these constants have mean value one, just like the(More)
  • 1