APPELL-LERCH SERIES VIEWED AS MOCK THETA FUNCTIONS

Zhang, Changgui

Type de document :

Pré-publication ou Document de travail

Titre :

APPELL-LERCH SERIES VIEWED AS MOCK THETA FUNCTIONS

Auteur(s) :

Zhang, Changgui [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

The goal of this paper is to prove that the quotient of a first order Appell-Lerch series by a suitable theta-function can be written, near every given root of unity, as the sum of two functions, one of which has a finite ...
Lire la suite >The goal of this paper is to prove that the quotient of a first order Appell-Lerch series by a suitable theta-function can be written, near every given root of unity, as the sum of two functions, one of which has a finite limit and the other one has an asymptotic behavior like as one Jacobi's theta-function when q tends to this root. In order to simplify the exposition, we propose the definition of what we mean almost theta-type function, false theta-type function and mock theta-type function. The utilization of continued fractions and linear fractional transformations plays a central role in this paper.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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APPELL-LERCH SERIES VIEWED AS MOCK THETA FUNCTIONS

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