Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis
| dc.creator | Khuri, N. N. | |
| dc.date | 2001-11-07 | |
| dc.date.accessioned | 2026-07-07T04:12:39Z | |
| dc.date.available | 2026-07-07T04:12:39Z | |
| dc.description | We use inverse scattering methods, generalized for a specific class of complex potentials, to construct a one parameter family of complex potentials V(s, r) which have the property that the zero energy s-wave Jost function, as a function of s alone, is identical to Riemann's $ξ$ function whose zeros are the non-trivial zeros of the zeta function. These potentials have an asymptotic expansion in inverse powers of s(s-1) with real coefficients V_n(r) which are explicitly calculated. We show that the validity of the Riemann hypothesis depends essentially on simple integrability properties of the first order coefficient, V_1(r). In the case studied in this paper, this coefficient does not satisfy these conditions, but proof of that fact does indicate several possibilities for proceeding further. | |
| dc.description | 107 pages, 1 figure, Latex | |
| dc.identifier | https://arxiv.org/abs/hep-th/0111067 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0111067 | |
| dc.identifier | Math.Phys.Anal.Geom. 5 (2002) 1-63 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/50973 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Number Theory | |
| dc.title | Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis | |
| dc.type | text |