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

Peter Jaksch

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arXiv · 2510.16759

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

Peter Jaksch

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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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Peter Jaksch. 2025-10-19. Successive generation of nontrivial Riemann zeros from a Wu-Sprung type potential. https://arxiv.org/abs/2510.16759

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