Successive generation of nontrivial Riemann zeros from a Wu-Sprung type potential

• URL: http://arxiv.org/abs/2510.16759v1
• Date: Sun, 19 Oct 2025 08:59:11 GMT
• Title: Successive generation of nontrivial Riemann zeros from a Wu-Sprung type potential
• Authors: Peter Jaksch,
• Abstract summary: A symmetric potential is generated for the 1D time-independent Schr"odinger equation.<n>The potential is generated as a series of correction functions.<n>It is found that the correction functions display a clear pattern that can be explained in simple terms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A series of numerical experiments are performed, where a symmetric potential is generated for the 1D time-independent Schr\"odinger equation, with an eigenspectrum that matches the imaginary part of the first nontrivial zeros of the Riemann Zeta Function. The potential is generated as a series of correction functions, where the starting point is a potential that matches the smooth Riemann -- von Mangoldt approximation. It is found that the correction functions display a clear pattern that can be explained in simple terms, almost entirely dependent on the approximation error in the Riemann -- von Mangoldt formula. This also provides an explanation for the fractal pattern in the potential that was observed by Wu and Sprung.

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