[Sur le comportement mock thêta de séries d'Appell–Lerch]
Le but de cette Note est de trouver une manière naturelle d'écrire chaque série d'Appell–Lerch du premier ordre au moyen de deux fonctions dont le comportement asymptotique devient plus simple. On démontre qu'une telle écriture existe, avec seulement des fonctions de type thêta et celles qui ont un développement asymptotique Gevrey. Afin de faciliter l'exposé, nous introduisons trois types de fonctions du genre thêta, qui seront appelés type thêta, type faux thêta et type mock thêta.
The goal of this paper is to find one natural way to write the first order Appell–Lerch series in terms of two functions whose asymptotic behavior becomes simple. It is shown that such writing exists, using only theta-like functions and functions having a Gevrey asymptotic expansion. In order of simplify the presentation, we introduce three types of theta-like functions that will be called theta-type, false theta-type and mock theta-type.
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@article{CRMATH_2015__353_12_1067_0,
author = {Zhang, Changgui},
title = {On the mock-theta behavior of {Appell{\textendash}Lerch} series},
journal = {Comptes Rendus. Math\'ematique},
pages = {1067--1073},
publisher = {Elsevier},
volume = {353},
number = {12},
year = {2015},
doi = {10.1016/j.crma.2015.09.028},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.09.028/}
}
TY - JOUR AU - Zhang, Changgui TI - On the mock-theta behavior of Appell–Lerch series JO - Comptes Rendus. Mathématique PY - 2015 SP - 1067 EP - 1073 VL - 353 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.09.028/ DO - 10.1016/j.crma.2015.09.028 LA - en ID - CRMATH_2015__353_12_1067_0 ER -
Zhang, Changgui. On the mock-theta behavior of Appell–Lerch series. Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1067-1073. doi : 10.1016/j.crma.2015.09.028. http://www.numdam.org/articles/10.1016/j.crma.2015.09.028/
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