Ground-State Negativity of Truncated Connes-Van Suijlekom Forms for Dirichlet L-Functions.

August 8, 2026Open Access

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The research aims to investigate the ground-state negativity of truncated Connes-van Suijlekom forms for real primitive Dirichlet L-functions.
Constructed the CvS kernel for real primitive Dirichlet characters.
Validated the kernel by comparing results to Hurwitz zeta functions.
Computed eigenvalues using ball arithmetic with explicit tail bounds.
The least eigenvalue λ_min of the truncated CvS form is negative and decreases with cutoff c (7≤c≤37, N=20).
All eigenvalue enclosures were computed in ball arithmetic under a resolution criterion.
Negativity of the truncated CvS quadratic form does not provide a positivity certificate related to the Generalized Riemann Hypothesis.

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Investigates ground-state negativity in Dirichlet L-functions using the CvS framework, implying new insights into spectral data.

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Ahmad Al Mohder (2026) studied this question.

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