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This is a Quantitative Study study.

September 30, 2025Comptes Rendus MathématiqueOpen Access

New eigenfunctions for the negative part of the Connes–Moscovici prolate spectrum

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This note demonstrates negative eigenvalues in the Connes–Moscovici prolate spectrum, suggesting a new method involving analytic functions.

Negative eigenvalues exhibiting ultraviolet behavior mimicking the Riemann zeta function's zeros are demonstrated.
Accurate computation of these eigenvalues is achieved using a new theory of analytic spectra.
The approach replaces Sturm–Liouville theory with complex analytic functions for determining spectral characteristics.
A simple equivalent definition of the non-classical part of the Connes–Moscovici spectrum reveals important eigenvalue information.

Ramis et al. (2025) studied this question.

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This note demonstrates negative eigenvalues in the Connes–Moscovici prolate spectrum, suggesting a new method involving analytic functions.