Weil quadratic form (앙드레 베유)에서 나온 basis로 연산자만들었는데 이 연산자로 소수 2,3,5,7,11,13으로 리만제타영점 50개를 수치적으로 정확하게 10E-3~10E-55 계산할수도 았고 연산자가 작용하는 스페이스 (길이랑 차원)을 무한대로 보낼때 리만제타 함수랑 같아지는데 이때 연산자가 positivity성질을 유지한다는것믄 보이면 리만가설 증명이된다고함

Zeta Spectral TriplesWe propose and investigate a strategy toward a proof of the Riemann Hypothesis based on a spectral realization of its non-trivial zeros. Our approach constructs self-adjoint operators obtained as rank-one perturbations of the spectral triple associated with the scaling operator on the interval $[λ^{-1}, λ]$. The construction only involves the Euler products over the primes $p \leq x = λ^2$ and produces self-adjoint operators whose spectra coincide, with striking numerical accuracy, with the lowest non-trivial zeros of $ζ(1/2 + i s)$, even for small values of $x$. The theoretical foundation rests on the framework introduced in "Spectral triples and zeta-cycles" (Enseign. Math. 69 (2023), no. 1-2, 93-148), together with the extension in "Quadratic Forms, Real Zeros and Echoes of the Spectral Action" (Commun. Math. Phys. (2025)) of the classical Caratheodory-Fejer theorem for Toeplitz matrices, which guarantees the necessary self-adjointness. Numerical experiments show that the spectra of the operators converge towards the zeros of $ζ(1/2 + i s)$ as the parameters $N, λ\to \infty$. A rigorous proof of this convergence would establish the Riemann Hypothesis. We further compute the regularized determinants of these operators and discuss the analytic role they play in controlling and potentially proving the above result by showing that, suitably normalized, they converge towards the Riemann $Ξ$ function.arxiv.org


알렝콘느 (비가환기하학 그사람 맞음) 가 쓴건데 왜캐 수학 커뮤니티 조용하냐

overflow reddit X mastodone bluesky 아무도 말이 없어서 당황함;;

콘느가 강연에서 이거 리만한테 컴퓨터 있었으면 이미 풀었을거라고하는데, 실제로 리만이 예측한 연산자의 basis가 Hermite basis인데 그걸로 Weil quadratic form에서 나온 basis가 공간이 작은 범위에서 근사가 잘되는거까지 확인함
먼가 이번 논문은 해석학이랑 연산자만 알면 이해할수있게 써놔서 검증 및 증명을 위해 계산레벨로 내려온게 아닌가싶음

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