A proof of the Riemann hypothesis

Details A proof of the Riemann hypothesis A proof of the Riemann hypothesis

2011-10-12

arxiv.org/abs/1110.2952v5

Mathematics

General Mathematics

14 pages

Scientific paper

The Riemann hypothesis was proved in this paper. First, a curve integral of the Riemann zeta function zeta(s) was formed, which is along a horizontal line from s to 1-\bar{s} which are two nontrivial zeros of zeta(s) and symmetric about the vertical line Re s=1/2. Next, the result of the curve integral was derived and proved equal to zero. Then, by proving a lemma of central dissymmetry of the Riemann zeta function zeta(s), two nontrivial zeros s and 1-\bar{s} were proved being a same zero or satisfying s=1-\bar{s}. Hence, the nontrivial zeros of zeta(s) all have real part Re s=1/2, that is, the Riemann hypothesis was proved.

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