Final steps towards a proof of the Riemann hypothesis
| dc.creator | Castro, Carlos | |
| dc.creator | Mahecha, Jorge | |
| dc.date | 2002-08-30 | |
| dc.date | 2002-11-05 | |
| dc.date.accessioned | 2026-07-07T04:14:03Z | |
| dc.date.available | 2026-07-07T04:14:03Z | |
| dc.description | A proof of the Riemann's hypothesis (RH) about the non-trivial zeros of the Riemann zeta-function is presented. It is based on the construction of an infinite family of operators D^{(k,l)} in one dimension, and their respective eigenfunctions ψ_s (t), parameterized by continuous real indexes k and l. Orthogonality of the eigenfunctions is connected to the zeros of the Riemann zeta-function. Due to the fundamental Gauss-Jacobi relation and the Riemann fundamental relation Z (s') = Z (1-s'), one can show that there is a direct concatenation among the following symmetries, t goes to 1/t, s goes to β- s (βa real), and s' goes to 1 - s', which establishes a one-to-one correspondence between the label s of one orthogonal state to a unique vacuum state, and a zero s' of the ζ. It is shown that the RH is a direct consequence of these symmetries, by arguing in particular that an exclusion of a continuum of the zeros of the Riemann zeta function results in the discrete set of the zeros located at the points s_n = 1/2 + i λ_n in the complex plane. | |
| dc.description | Latex file, 18 pages, revised text, stronger and improved arguments with a figure are added, submitted to Annals of Mathematics | |
| dc.identifier | https://arxiv.org/abs/hep-th/0208221 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0208221 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/51483 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | General Mathematics | |
| dc.title | Final steps towards a proof of the Riemann hypothesis | |
| dc.type | text |