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In mathematics, a mock modular form is the … 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.turns them into harmonic weak Maass forms.
, En mathématiques, et plus précisément en a … 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.ses fonctions thêta et les formes de Maas.
, Le funzioni mock theta fanno parte di un i … 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.himici ed anche nelle ricerche sul cancro.
, Inom matematiken är en falsk modulär form … 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.lar dem till harmoniska svaga Maassformer.
, En matemáticas, una forma modular simulada … 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.erte en formas armónicas débiles de Maass.
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"Suppose there is a function in the Euleri … "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."o, I call the function a Mock θ-function."
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En matemáticas, una forma modular simulada … 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.erte en formas armónicas débiles de Maass.
, Inom matematiken är en falsk modulär form … 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.lar dem till harmoniska svaga Maassformer.
, En mathématiques, et plus précisément en a … 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.ses fonctions thêta et les formes de Maas.
, In mathematics, a mock modular form is the … 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.turns them into harmonic weak Maass forms.
, Le funzioni mock theta fanno parte di un i … 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.cedimento di come possano essere derivate.
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Funzione mock theta
, Mock modular form
, Fausse fonction thêta
, Falsk modulär form
, Forma modular simulada
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