The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
Abstract
Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace formula and eliminates the parameter $ \delta $ of our previous approach.
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Citations
Cites
Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
Slepian, D., & Pollak, H. O. (1961) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1961.tb03976.x · Cited by 2,492
Connes, A., Cuntz, J., & Rieffel, M. A. (2010) · Oberwolfach Reports · doi:10.4171/owr/2009/41 · Cited by 2,268
Self-citationWEIL, A. A. (1967) · Springer eBooks · doi:10.1007/978-1-4612-9834-2 · Cited by 1,223
Sur certains groupes d'opérateurs unitaires
Weil, A. (1964) · Acta Mathematica · doi:10.1007/bf02391012 · Cited by 1,061
Landau, H. J., & Pollak, H. O. (1962) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1962.tb03279.x · Cited by 839
Guillemin, V., & Sternberg, S. (1977) · Mathematical Surveys and Monographs · doi:10.1090/surv/014 · Cited by 747
A Lefschetz Fixed Point Formula for Elliptic Complexes: I
Atiyah, M. F., & Bott, R. (1967) · The Annals of Mathematics · doi:10.2307/1970694 · Cited by 476
Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics
(1982) · Lecture Notes in Physics · doi:10.1007/3-540-11559-5 · Cited by 421
Bost, J. B., & Connes, A. (1995) · Selecta Mathematica · doi:10.1007/bf01589495 · Cited by 308
Self-citationSome Asymptotic Expansions for Prolate Spheroidal Wave Functions
Slepian, D. (1965) · Journal of Mathematics and Physics · doi:10.1002/sapm196544199 · Cited by 261
Metadata
- Authors
- Connes, A.
- Venue
- Selecta Mathematica
- Published
- 1999-04
- Volume
- 5
- Issue
- 1
- Pages
- 29-106
- ISSN
- 1022-1824 (ISSN-L)
- 1420-9020
- OpenAlex
- W2147436369
- Cited by
- 339
- References
- 14
- FWCI
- 17.21
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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