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A proof of Riemann Hypothesis

General Mathematics 2024-06-07 v7

Abstract

Let Ξ(t)\Xi(t) be a function relating to the Riemann zeta function ζ(s)\zeta (s) with s=12+its = \frac{1} {2} + it. In this paper, we construct a function vv containing tt and Ξ(t)\Xi(t), and prove that vv satisfies a nonadjoint boundary value problem to a nonsingular differential equation if tt is any nontrivial zero of Ξ(t)\Xi(t). Inspecting properties of vv and using known results of nontrivial zeros of ζ(s)\zeta (s), we derive that nontrivial zeros of ζ(s)\zeta (s) all have real part equal to 12\frac{1} {2}, which concludes that Riemann Hypothesis is true.

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Cite

@article{arxiv.1704.05747,
  title  = {A proof of Riemann Hypothesis},
  author = {Pengcheng Niu and Junli Zhang},
  journal= {arXiv preprint arXiv:1704.05747},
  year   = {2024}
}

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15Pages

R2 v1 2026-06-22T19:21:26.967Z