For example, consider a subset X of {0,1} specified by the following rule: 0 belongs to X if and only if the Riemann hypothesis is true, and 1 belongs to X if and only if the Riemann hypothesis is false.
In 1997 Deshouillers, Effinger, te Riele, and Zinoviev showed that the generalized Riemann hypothesis implies that every odd number greater than 5 is the sum of three primes.
The story makes reference to the Riemann hypothesis, featuring a sequence set in a 'world' modelled on the Riemann zeta function.
It focuses on the proof, without going fully into the rigorous how-to details, gives examples of some highly interesting and famous proofs, as well as the outstanding problems of mathematics (the Riemann hypothesis, etc.), and goes on to speculate on what a proof really means, in relationship to actual truth.
Bernhard Riemann | Riemann zeta function | Riemann surface | Riemann hypothesis | Alvarez hypothesis | Witch-cult hypothesis | extraterrestrial hypothesis | two-source hypothesis | Riemann sphere | Riemann solver | Riemann-Roch theorem | Rare Earth hypothesis | Hugo Riemann | Hebrew Gospel hypothesis | Articulata hypothesis | Warburg hypothesis | Two-source hypothesis | Turnover-pulse hypothesis | Three-source hypothesis | Swoon hypothesis | Stolen body hypothesis | Statistical hypothesis testing | Schinzel's hypothesis H | Riemann Xi function | Riemann's function | Riemann's existence theorem | Riemann–Roch theorem | Riemann manifold | Riemann integral | Riemann |
Numerical tests of the Riemann hypothesis use this technique to get an upper bound for the number of zeros of Franz Mertens
The Mertens conjecture concerning its growth, conjecturing it bounded by x1/2, which would have implied the Riemann hypothesis, is now known to be false (Odlyzko and te Riele, 1985).
For the case of the Riemann zeros Wu and Sprung and others have shown that the potential can be written implicitly in terms of the Gamma function and zeroth-order Bessel function.
In the early 20th century G. H. Hardy and Littlewood proved many results about the zeta function in an attempt to prove the Riemann Hypothesis.