A Strategy for Proving Riemann Hypothesis
| dc.creator | Pitkanen, Matti | |
| dc.date | 2001-11-26 | |
| dc.date | 2002-01-25 | |
| dc.date.accessioned | 2026-07-07T04:44:46Z | |
| dc.date.available | 2026-07-07T04:44:46Z | |
| dc.description | A strategy for proving Riemann hypothesis is suggested. The vanishing of the Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator $D^+$ having the zeros of Riemann Zeta as its eigenvalues. The construction of $D^+$ is inspired by the conviction that Riemann Zeta is associated with a physical system allowing conformal transformations as its symmetries. The eigenfunctions of $D^+$ are analogous to the so called coherent states and in general not orthogonal to each other. The states orthogonal to a vacuum state (which has a negative norm squared) correspond to the zeros of the Riemann Zeta. The induced metric in the space ${\cal{V}}$ of states which correspond to the zeros of the Riemann Zeta at the critical line $Re[s]=1/2$ is hermitian and both hermiticity and positive definiteness properties imply Riemann hypothesis. Conformal invariance in the sense of gauge invariance allows only the states belonging to ${\cal{V}}$. Riemann hypothesis follows also from a restricted form of a dynamical conformal invariance in ${\cal{V}}$ and one can reduce the proof to a standard analytic argument used in Lie group theory. | |
| dc.description | 14 pages, realization that positive definiteness of the metric is possible and also implies Riemann hypothesis, Lie group theoretic analytic argument proving Riemann hypothesis | |
| dc.identifier | https://arxiv.org/abs/math/0111262 | |
| dc.identifier | http://arxiv.org/abs/math/0111262 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62726 | |
| dc.subject | General Mathematics | |
| dc.title | A Strategy for Proving Riemann Hypothesis | |
| dc.type | text |