Equivalence · version 1
Earlier version 1. View current version 3 →
For the classical de Bruijn–Newman constant, RH is equivalent to Λ = 0. Λ is defined by H_t(z) = ∫₀∞ exp(tu²) Φ(u) cos(zu) du, using the classical Riemann kernel Φ and normalization in the cited paper; all H_t zeros are real exactly when t ≥ Λ.
The equivalence is a theorem; whether the constant is zero remains the unresolved target.
Open
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Rodgers–Tao · Newman constant is nonnegative · §1: RH iff Λ ≤ 0; Theorem 1.1: Λ ≥ 0 →
Source dated Jul 3, 2021 · Observed Oct 10, 2026
In this problem · publication v3 · Selected context
Equivalent formulation · Open
Neither the lower bound Λ ≥ 0 nor a positive upper bound supplies Λ = 0. These are formulations of one Problem, not separate RH problems.
Relationship not independently reviewed. This concerns its use in this problem.
After the nonnegativity theorem, RH is equivalent to Λ = 0.
paraphrase · No upstream full text or code is republished by this record.
Brad Rodgers · Terence Tao · Published
Published in Forum of Mathematics, Pi (2020). The pinned 2021 author revision records a correction to Section 8; earlier manuscript history is not silently substituted.
Source revision: arxiv-v5. Observed Oct 10, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Source updated Jul 3, 2021.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Open
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Source dated Jul 3, 2021 · Observed Oct 10, 2026 · Source passage →