the "encoding" of the distribution of primes by the zeros
of the Riemann zeta function
Riemann showed that the [nontrivial] zeros of [the
zeta function] determine the fluctuations in the density of primes (that
is their importance) and conjectured that they all have real part 1/2."
M.V. Berry, from "Quantum
Chaology", The Bakerian Lecture 1987, Proceedings of the Royal Society of
London A 413 (1987) 183–198
"...the complex zeros of the Riemann zeta-function induce the local
variations in the distribution of the primes."
Hans Riesel from Prime Numbers and Computer Methods for Factorisation (Birkhaüser, 1994)
There are two approaches:
the more common approach
the more elegant approach
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