The UV prolate spectrum matches the zeros of zeta-Reference-Cited by-同舟云学术

The UV prolate spectrum matches the zeros of zeta

Published:2022-05-24 Issue:22 Volume:119 Page:
ISSN:0027-8424
Container-title:Proceedings of the National Academy of Sciences
language:en
Short-container-title:Proc. Natl. Acad. Sci. U.S.A.

Author:

Connes Alain¹²,Moscovici Henri³^ORCID

Affiliation:

1. Collège de France, 75005 Paris, France

2. Institut des Hautes Etudes Scientifiques, 91440 Bures-sur-Yvette, France

3. Department of Mathematics, The Ohio State University, Columbus, OH 43210

Abstract

Significance We show that the eigenvalues of the self-adjoint extension (introduced by A.C. in 1998) of the prolate spheroidal operator reproduce the UV behavior of the squares of zeros of the Riemann zeta function, and we construct an isospectral family of Dirac operators whose spectra have the same UV behavior as those zeros.

Publisher

Proceedings of the National Academy of Sciences

Subject

Multidisciplinary

Link

https://pnas.org/doi/pdf/10.1073/pnas.2123174119

Reference24 articles.

1. Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

2. Weil positivity and trace formula the archimedean place

3. A. Connes C. Consani Spectral triples and zeta-cycles. arXiv [Preprint] (2021). https://doi.org/10.48550/arXiv:2106.01715. Accessed 3 June 2021.

4. Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions

5. Some Asymptotic Expansions for Prolate Spheroidal Wave Functions

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