Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis

Details Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis

2001-11-07

arxiv.org/abs/hep-th/0111067v1

Math.Phys.Anal.Geom. 5 (2002) 1-63

Physics

High Energy Physics

High Energy Physics - Theory

107 pages, 1 figure, Latex

Scientific paper

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 $\xi$ 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.

Affiliated with

Also associated with

No associations

Rating

Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-102791