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This is fairly straightforward. It's basically a matter of generalisation. Riemann put forward an explicit formula
(proved rigorously by von
Mangoldt) which relates a prime counting function and a sum over the
zeros of the Riemann zeta function in The Riemann-Weil Explicit Formula (1952) generalises this. Burnol points out that it generalises the Riemann-von Mangoldt formula to an identity between two distributions. He goes on: "In fact Weil's aim in this regard seems to have been at first to express 'the most general' Riemann-like relation between primes and zeros. One can argue whether such a thing exists, and more strongly still whether it really has been achieved by Weil." The formula in [1952] applies to a general algebraic number field
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