Mean Staircase of the Riemann Zeros: a comment on the Lambert W function and an algebraic aspect
| dc.creator | Marca, Davide a | |
| dc.creator | Beltraminelli, Stefano | |
| dc.creator | Merlini, Danilo | |
| dc.date | 2009-01-21 | |
| dc.date.accessioned | 2026-07-07T12:32:54Z | |
| dc.date.available | 2026-07-07T12:32:54Z | |
| dc.description | In this note we discuss explicitly the structure of two simple set of zeros which are associated with the mean staircase emerging from the zeta function and we specify a solution using the Lambert W function. The argument of it may then be set equal to a special $N \times N$ classical matrix (for every $N$) related to the Hamiltonian of the Mehta-Dyson model. In this way we specify a function of an hermitean operator whose eigenvalues are the "trivial zeros" on the critical line. The first set of trivial zeros is defined by the relations $\tmop{Im} (ζ({1/2} + i \cdot t)) = 0 \wedge \tmop{Re} (ζ({1/2} + i \cdot t)) \neq 0$ and viceversa for the second set. (To distinguish from the usual trivial zeros $s = ρ+ i \cdot t = - 2 n$, $n \geqslant 1$ integer) | |
| dc.identifier | https://arxiv.org/abs/0901.3377 | |
| dc.identifier | http://arxiv.org/abs/0901.3377 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216940 | |
| dc.subject | Number Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 11M26, 81Q10 | |
| dc.title | Mean Staircase of the Riemann Zeros: a comment on the Lambert W function and an algebraic aspect | |
| dc.type | text |