ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)∞

doi:10.1007/s10473-021-0617-z

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 2086-2106.doi: 10.1007/s10473-021-0617-z

ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞

Changgui ZHANG

Laboratoire P. Painlevé(UMR-CNRS 8524), Département de mathématiques, FST, Université de Lille, Cité scientifique, 59655 Villeneuve d'Ascq cedex, France

收稿日期:2021-05-06 修回日期:2021-08-11 出版日期:2021-12-25 发布日期:2021-12-27
作者简介:Changgui ZHANG,E-mail:changgui.zhang@univ-lille.fr
基金资助:
The author was supported by Labex CEMPI (Centre Européen pour les Mathémmatiques, la Physique et leurs Interaction).

ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞

Changgui ZHANG

Laboratoire P. Painlevé(UMR-CNRS 8524), Département de mathématiques, FST, Université de Lille, Cité scientifique, 59655 Villeneuve d'Ascq cedex, France

Received:2021-05-06 Revised:2021-08-11 Online:2021-12-25 Published:2021-12-27
Supported by:
The author was supported by Labex CEMPI (Centre Européen pour les Mathémmatiques, la Physique et leurs Interaction).

摘要/Abstract

摘要： As in our previous work[14], a function is said to be of theta-type when its asymptotic behavior near any root of unity is similar to what happened for Jacobi theta functions. It is shown that only four Euler infinite products have this property. That this is the case is obtained by investigating the analyticity obstacle of a Laplace-type integral of the exponential generating function of Bernoulli numbers.

关键词: q-series, Mock theta-functions, Stokes phenomenon, continued fractions

Abstract: As in our previous work[14], a function is said to be of theta-type when its asymptotic behavior near any root of unity is similar to what happened for Jacobi theta functions. It is shown that only four Euler infinite products have this property. That this is the case is obtained by investigating the analyticity obstacle of a Laplace-type integral of the exponential generating function of Bernoulli numbers.

Key words: q-series, Mock theta-functions, Stokes phenomenon, continued fractions

中图分类号:

34M30

Changgui ZHANG. ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞[J]. 数学物理学报(英文版), 2021, 41(6): 2086-2106.

Changgui ZHANG. ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞[J]. Acta mathematica scientia,Series B, 2021, 41(6): 2086-2106.

参考文献 15

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ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞

ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞

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