arXiv:2006.12546math.GM
The Riemann Hypothesis is false
Abstract
Let $Θ$ denote the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate that $Θ=1$, which entails the existence of infinitely many Riemann zeros off the critical line (thus disproving the Riemann Hypothesis (RH), which asserts that $Θ= \frac{1}{2}$). The paper is concluded by a brief discussion of why our argument doesn't work for both Weil and Beurling zeta functions whose analogues of the RH are known to be true. NB: The author believes that the paper is now clear and rigorous enough for someone with at least a graduate level of familirity with analytic number theory. Therefore, this shall be the very final revision. Addendum (11 February 2026): On page 4 of the previous version (version 47), there is a minor typo where the author wrote F''(x_0)=-v^{2}/T instead of F''(x_0) = -(v/T)^2. A correction of this typo reveals that the stationery phase approximation (SPA) gives a weak upper bound for J_{0}(T) when x_0 is small. The latest (and final) version circumvents the use of the SPA by directly summing J(T) over m, and taking the summation inside the integral (equation (20)). This allows us to invoke Van de Corput-type bounds, which are uniformly sharp for our purposes. The rest of the paper remains as it was.
No and this post will hopefully be flagged soon. A quick Google search of the author would also show that they have published several similar proofs before [0] which were also wrong. [0]: https://arxiv.org/abs/2006.12546
mjreacherView on HNParent context
This is actually the 19th version of the paper the author has published in just over 2 years: https://arxiv.org/abs/2006.12546 Being such a short paper if people in this field thought it was close to actually disproving the Riemann Hypothesis likely another mathematician could…
oblvious-earthView on HNParent context
This was a review of the author's earlier paper of 2018, in which they were actually claiming a proof of RH. On their arXiv page: https://arxiv.org/abs/2006.12546, the author states that "though all my previous proposed (dis)proofs were flawed, i think the flaws pointed me…
Quant10View on HNParent context
This was a review of the author's earlier paper of 2018, in which they were actually claiming a proof of the RH. On their arXiv page: https://arxiv.org/abs/2006.12546, the author states that "though all my previous proposed (dis)proofs were flawed, i think the flaws pointed me…
Quant10View on HNParent context
I wouldn't know. But from the author's arXiv statement [1] that ..though all of my previous (dis)proofs were flawed, i think the flaws pointed me towards the right direction..." it seems they are quite confident in the current version. [1] https://arxiv.org/abs/2006.12546
Quant10View on HNParent context