Taylor coefficients of the Jacobi θ3(q) function

被引：3

作者：

Wakhare, Tanay ^{[1
]}

Vignat, Christophe ^{[2
,3
]}

机构：

[1] Univ Maryland, College Pk, MD 20742 USA

[2] Univ Paris Sud, Cent Supelec, LSS, Orsay, France

[3] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

来源：

JOURNAL OF NUMBER THEORY | 2020年 / 216卷

关键词：

Jacobi theta function; Discrete Gaussian distribution; Elliptic functions;

D O I：

10.1016/j.jnt.2020.03.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend some results recently obtained by Dan Romik [14] about the Taylor coefficients of the theta function theta(3)(e(-pi)) to the case theta(3)(q) of a real valued variable 0 < q < 1. These results are obtained by carefully studying the properties of the cumulants associated to a Jacobi theta(3) (or discrete normal) distributed random variable. This article also states some integrality conjectures about rational sequences that generalize the one studied by Romik. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：280 / 306

页数：27

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