Mock modular form (original) (raw)
En matemáticas, una forma modular simulada es la parte holomórfica de una débil armónica, y una función theta simulada es esencialmente una forma modular simulada de peso 1/2. Srinivasa Ramanujan describió los primeros ejemplos de funciones theta simuladas en su última carta de 1920 a G. H. Hardy y en su cuaderno perdido. Sander Zwegers descubrió que agregarles ciertas funciones no holomorfas las convierte en formas armónicas débiles de Maass.
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| dbo:abstract | En matemáticas, una forma modular simulada es la parte holomórfica de una débil armónica, y una función theta simulada es esencialmente una forma modular simulada de peso 1/2. Srinivasa Ramanujan describió los primeros ejemplos de funciones theta simuladas en su última carta de 1920 a G. H. Hardy y en su cuaderno perdido. Sander Zwegers descubrió que agregarles ciertas funciones no holomorfas las convierte en formas armónicas débiles de Maass. (es) In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1/2. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Sander Zwegers discovered that adding certain non-holomorphic functions to them turns them into harmonic weak Maass forms. (en) En mathématiques, et plus précisément en analyse, une fausse forme modulaire est la partie holomorphe d'une (en) harmonique, et une fausse fonction thêta est essentiellement une fausse forme modulaire de poids 1/2. Les premiers exemples de fausses fonctions thêta furent décrits par Srinivasa Ramanujan dans sa dernière lettre à Godfrey Harold Hardy (en 1920) et dans son cahier perdu ; il a découvert alors que ces fonctions se comportent en partie comme les fonctions thêta, d'où leur nom (mock theta functions en anglais). (en) découvrit en 2001 la relation entre les fausses fonctions thêta et les formes de Maas. (fr) Le funzioni mock theta fanno parte di un insieme di funzioni, nominate da Srinivasa Ramanujan, nel campo della teoria dei numeri e delle funzioni modulari, in una lettera scritta in punto di morte a G. H. Hardy e probabilmente descritte in un suo quaderno di appunti andato perduto. Della lettera si sono però perse le prime pagine. Per questa ragione del lavoro di Ramanujan rimangono solo 17 esempi, e mancano una definizione formale e il procedimento di come possano essere derivate. Le funzioni mock theta costituiscono una serie infinita di numeri, probabilmente correlate alle funzioni theta, note da secoli e usate in un gran numero di problemi e analisi matematiche. In particolare, comportamenti descrivibili con funzioni mock theta sono oggi stati individuati in diversi campi: nei calcoli matematici, fisici, chimici ed anche nelle ricerche sul cancro. (it) Inom matematiken är en falsk modulär form den analytiska delen av en harmonisk svag Maassform och en falsk thetafunktion är en falsk modulär form av vikt 1/2. De första exemplen av falska thetafunktioner beskrevs av Srinivasa Ramanujan i hans sista brev till G. H. Hardy, skickat 1920. upptäckte 2002 att genom att addera vissa icke-analytiska funktioner till dem förvandlar dem till harmoniska svaga Maassformer. (sv) |
| dbo:wikiPageExternalLink | http://igitur-archive.library.uu.nl/dissertations/2003-0127-094324/inhoud.htm http://mathsci.ucd.ie/~zwegers/presentations/002.pdf https://afolsom.people.amherst.edu/BringmannFolsomOno-Compositio.pdf https://uva.theopenscholar.com/files/ken-ono/files/098_8.pdf https://uva.theopenscholar.com/files/ken-ono/files/100_8.pdf http://www.mi.uni-koeln.de/~kbringma/papers.html http://people.mpim-bonn.mpg.de/zagier/files/aster/326/fulltext.pdf http://mathsci.ucd.ie/~zwegers/papers/001.pdf http://journals.cambridge.org/action/displayAbstract%3Faid=63263 https://web.archive.org/web/20081023234404/http:/mathsci.ucd.ie/~zwegers/ https://web.archive.org/web/20081204111537/http:/www.math.psu.edu/andrews/biblio.html https://web.archive.org/web/20081221143605/http:/www.mpim-bonn.mpg.de/Events/This+Year+and+Prospect/Mock+theta+functions/ https://web.archive.org/web/20100620082612/http:/www.math.wisc.edu/~ono/reprints/index.html |
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| dbp:align | right (en) |
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| dbp:date | January 2021 (en) February 2018 (en) |
| dbp:fixAttempted | yes (en) |
| dbp:quote | "Suppose there is a function in the Eulerian form and suppose that all or an infinity of points are exponential singularities, and also suppose that at these points the asymptotic form closes as neatly as in the cases of and . The question is: Is the function taken the sum of two functions one of which is an ordinary θ-function and the other a function which is O at all the points e2mi/n? ... When it is not so, I call the function a Mock θ-function." (en) |
| dbp:reason | Parenthetical referencing has been deprecated; convert to shortened footnotes. (en) |
| dbp:source | Ramanujan's original definition of a mock theta function (en) |
| dbp:title | Mock Theta Function (en) |
| dbp:urlname | MockThetaFunction (en) |
| dbp:width | 33.0 (dbd:perCent) |
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| rdfs:comment | En matemáticas, una forma modular simulada es la parte holomórfica de una débil armónica, y una función theta simulada es esencialmente una forma modular simulada de peso 1/2. Srinivasa Ramanujan describió los primeros ejemplos de funciones theta simuladas en su última carta de 1920 a G. H. Hardy y en su cuaderno perdido. Sander Zwegers descubrió que agregarles ciertas funciones no holomorfas las convierte en formas armónicas débiles de Maass. (es) In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1/2. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Sander Zwegers discovered that adding certain non-holomorphic functions to them turns them into harmonic weak Maass forms. (en) En mathématiques, et plus précisément en analyse, une fausse forme modulaire est la partie holomorphe d'une (en) harmonique, et une fausse fonction thêta est essentiellement une fausse forme modulaire de poids 1/2. Les premiers exemples de fausses fonctions thêta furent décrits par Srinivasa Ramanujan dans sa dernière lettre à Godfrey Harold Hardy (en 1920) et dans son cahier perdu ; il a découvert alors que ces fonctions se comportent en partie comme les fonctions thêta, d'où leur nom (mock theta functions en anglais). (en) découvrit en 2001 la relation entre les fausses fonctions thêta et les formes de Maas. (fr) Inom matematiken är en falsk modulär form den analytiska delen av en harmonisk svag Maassform och en falsk thetafunktion är en falsk modulär form av vikt 1/2. De första exemplen av falska thetafunktioner beskrevs av Srinivasa Ramanujan i hans sista brev till G. H. Hardy, skickat 1920. upptäckte 2002 att genom att addera vissa icke-analytiska funktioner till dem förvandlar dem till harmoniska svaga Maassformer. (sv) Le funzioni mock theta fanno parte di un insieme di funzioni, nominate da Srinivasa Ramanujan, nel campo della teoria dei numeri e delle funzioni modulari, in una lettera scritta in punto di morte a G. H. Hardy e probabilmente descritte in un suo quaderno di appunti andato perduto. Della lettera si sono però perse le prime pagine. Per questa ragione del lavoro di Ramanujan rimangono solo 17 esempi, e mancano una definizione formale e il procedimento di come possano essere derivate. (it) |
| rdfs:label | Forma modular simulada (es) Funzione mock theta (it) Fausse fonction thêta (fr) Mock modular form (en) Falsk modulär form (sv) |
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