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Taking r > 0, let π 2r (x) denote the number of prime pairs (p, p + 2r) with p ≤ x. The prime-pair conjecture of Hardy and Littlewood (1923) asserts that π 2r (x) ∼ 2C 2r li 2 (x) with an explicit constant C 2r > 0. There seems to be no good conjecture for the remainders ω 2r (x) = π 2r (x)−2C 2r li 2 (x) that corresponds to Riemann's formula for… (More)

- Jaap Korevaar
- 2013

There are parallels between de Bruijn's early work in analysis and that of the author. However, Dick's work soon became much broader and deeper. While the present paper reviews several topics of common interest, its main content is a short version of Dick's important article related to Riemann's Hypothesis, entitled 'The roots of trigonometric integrals'… (More)

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