What question did this study set out to answer?

The aim is to establish unconditional results related to the spectral bounds of the Laplacian derived from Riemann zeros.

April 14, 20260 citationsOpen Access

Quantitative Spectral Bounds for the Riemann Zero Log-Gas Laplacian

Quantitative Spectral Bounds for the Riemann Zero Log-Gas Laplacian, an Unconditional Prime Sum Identity, and a Program Summary

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New unconditional results demonstrate exact spectral bounds in the context of prime sums and Riemann zeros, suggesting further inquiry is needed.

The aim is to establish unconditional results related to the spectral bounds of the Laplacian derived from Riemann zeros.
Developed two unconditional results for the graph Laplacian based on the first N Riemann zeros.
Proved the identity TrHad(N) = Pfull(N) + 2N¯ BN without assuming the Riemann Hypothesis.
Applied Selberg’s zero-gap theorem for lower bounds and introduced new methods for upper bounds on spectral gap.
Established lower bound λ2(LN ) ≥ π2/(N2 δ2 j ) using existing theorems.
Derive new upper bound λ2(LN ) ≤ 12 j<k (j−k)2/(γj−γk )2/[N(N2 −1)].
Identified that the upper bound remains numerically tight for N ≤50.

Devin Wright (2026) studied this question.

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April 14, 20260 citationsOpen Access

Quantitative Spectral Bounds for the Riemann Zero Log-Gas Laplacian, an Unconditional Prime Sum Identity, and a Program Summary

View Full Paper

Ask AI

Bookmark

Authors

New unconditional results demonstrate exact spectral bounds in the context of prime sums and Riemann zeros, suggesting further inquiry is needed.

The aim is to establish unconditional results related to the spectral bounds of the Laplacian derived from Riemann zeros.
Developed two unconditional results for the graph Laplacian based on the first N Riemann zeros.
Proved the identity TrHad(N) = Pfull(N) + 2N¯ BN without assuming the Riemann Hypothesis.
Applied Selberg’s zero-gap theorem for lower bounds and introduced new methods for upper bounds on spectral gap.
Established lower bound λ2(LN ) ≥ π2/(N2 δ2 j ) using existing theorems.
Derive new upper bound λ2(LN ) ≤ 12 j<k (j−k)2/(γj−γk )2/[N(N2 −1)].
Identified that the upper bound remains numerically tight for N ≤50.

Devin Wright (2026) studied this question.

View Full Paper

Ask AI

Bookmark