Number Theory


Disproof of the Riemann Hypothesis

Authors: Igor Hrnčić

This paper disproves the Riemann hypothesis by analyzing the integral representation of the Riemann zeta function that converges absolutely in the root-free region. The analysis is performed upon the well known inverse Mellin transform of zeta, that defines the Mertens function. The contour of integration is taken arbitrarily close to the nontrivial roots, and then only arbitrarily small parts of the integrand that are infinitely close to the nontrivial roots on such contour are analyzed. The convergence of the integral at hand then implies a result that a series over the derivative of zeta and over nontrivial roots closest to the roots free region converges. This result is in a contradiction with the well known result that the very same series, when taken over the critical line and under the truth of the Riemann hypothesis, diverges. This disproves the Riemann hypothesis.

Comments: 6 Pages.

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Submission history

[v1] 2018-03-12 09:55:34

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