Comments on the Riemann conjecture and index theory on Cantorian fractal space-time
ABSTRACT: An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show us...
- Autores:
-
Mahecha Gómez, Jorge Eduardo
Castro Perelman, Carlos
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2002
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/39812
- Acceso en línea:
- https://hdl.handle.net/10495/39812
- Palabra clave:
- Riemann hypothesis
Index theory (Mathematics)
Spectral theory (Mathematics)
Heurística
Heuristics
Fractales
Fractals
Espacio y tiempo
Space and time
http://id.loc.gov/authorities/subjects/sh2005000907
http://id.loc.gov/authorities/subjects/sh85064861
http://id.loc.gov/authorities/subjects/sh85126408
https://id.nlm.nih.gov/mesh/D000066506
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/2.5/co/
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| dc.title.spa.fl_str_mv |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| title |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| spellingShingle |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time Riemann hypothesis Index theory (Mathematics) Spectral theory (Mathematics) Heurística Heuristics Fractales Fractals Espacio y tiempo Space and time http://id.loc.gov/authorities/subjects/sh2005000907 http://id.loc.gov/authorities/subjects/sh85064861 http://id.loc.gov/authorities/subjects/sh85126408 https://id.nlm.nih.gov/mesh/D000066506 |
| title_short |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| title_full |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| title_fullStr |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| title_full_unstemmed |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| title_sort |
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time |
| dc.creator.fl_str_mv |
Mahecha Gómez, Jorge Eduardo Castro Perelman, Carlos |
| dc.contributor.author.none.fl_str_mv |
Mahecha Gómez, Jorge Eduardo Castro Perelman, Carlos |
| dc.contributor.researchgroup.spa.fl_str_mv |
Grupo de Física Atómica y Molecular |
| dc.subject.lcsh.none.fl_str_mv |
Riemann hypothesis Index theory (Mathematics) Spectral theory (Mathematics) |
| topic |
Riemann hypothesis Index theory (Mathematics) Spectral theory (Mathematics) Heurística Heuristics Fractales Fractals Espacio y tiempo Space and time http://id.loc.gov/authorities/subjects/sh2005000907 http://id.loc.gov/authorities/subjects/sh85064861 http://id.loc.gov/authorities/subjects/sh85126408 https://id.nlm.nih.gov/mesh/D000066506 |
| dc.subject.decs.none.fl_str_mv |
Heurística Heuristics |
| dc.subject.lemb.none.fl_str_mv |
Fractales Fractals Espacio y tiempo Space and time |
| dc.subject.lcshuri.none.fl_str_mv |
http://id.loc.gov/authorities/subjects/sh2005000907 http://id.loc.gov/authorities/subjects/sh85064861 http://id.loc.gov/authorities/subjects/sh85126408 |
| dc.subject.meshuri.none.fl_str_mv |
https://id.nlm.nih.gov/mesh/D000066506 |
| description |
ABSTRACT: An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal branes living in Cantorian-fractal space- time, how the required negative traces associated with those derivative operators naturally agree with the zeta function evaluated at the spectral dimensions. The ζ(0) = −1/2 plays a fundamental role. Final remarks on the recent developments in the proof of the Riemann conjecture are made. |
| publishDate |
2002 |
| dc.date.issued.none.fl_str_mv |
2002 |
| dc.date.accessioned.none.fl_str_mv |
2024-06-09T12:42:04Z |
| dc.date.available.none.fl_str_mv |
2024-06-09T12:42:04Z |
| dc.type.spa.fl_str_mv |
Artículo de investigación |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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https://purl.org/redcol/resource_type/ART |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/acceptedVersion |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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acceptedVersion |
| dc.identifier.issn.none.fl_str_mv |
0960-0779 10.1016/S0960-0779(01)00124-2 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/10495/39812 |
| dc.identifier.eissn.none.fl_str_mv |
1873-2887 |
| identifier_str_mv |
0960-0779 10.1016/S0960-0779(01)00124-2 1873-2887 |
| url |
https://hdl.handle.net/10495/39812 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartofjournalabbrev.spa.fl_str_mv |
Chaos. Solitons. Fractals. |
| dc.relation.citationendpage.spa.fl_str_mv |
21 |
| dc.relation.citationissue.spa.fl_str_mv |
7 |
| dc.relation.citationstartpage.spa.fl_str_mv |
1 |
| dc.relation.citationvolume.spa.fl_str_mv |
13 |
| dc.relation.ispartofjournal.spa.fl_str_mv |
Chaos, Solitons and Fractals |
| dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/2.5/co/ |
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https://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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openAccess |
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22 páginas |
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application/pdf |
| dc.publisher.spa.fl_str_mv |
Elsevier |
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Oxford, Inglaterra |
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Universidad de Antioquia |
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Mahecha Gómez, Jorge EduardoCastro Perelman, CarlosGrupo de Física Atómica y Molecular2024-06-09T12:42:04Z2024-06-09T12:42:04Z20020960-077910.1016/S0960-0779(01)00124-2https://hdl.handle.net/10495/398121873-2887ABSTRACT: An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal branes living in Cantorian-fractal space- time, how the required negative traces associated with those derivative operators naturally agree with the zeta function evaluated at the spectral dimensions. The ζ(0) = −1/2 plays a fundamental role. Final remarks on the recent developments in the proof of the Riemann conjecture are made.COL000844122 páginasapplication/pdfengElsevierOxford, Inglaterrahttp://creativecommons.org/licenses/by-nc-nd/2.5/co/https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Riemann hypothesisIndex theory (Mathematics)Spectral theory (Mathematics)HeurísticaHeuristicsFractalesFractalsEspacio y tiempoSpace and timehttp://id.loc.gov/authorities/subjects/sh2005000907http://id.loc.gov/authorities/subjects/sh85064861http://id.loc.gov/authorities/subjects/sh85126408https://id.nlm.nih.gov/mesh/D000066506Comments on the Riemann conjecture and index theory on Cantorian fractal space-timeArtículo de investigaciónhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionChaos. Solitons. 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