Truncated theta series and a problem of Guo and Zeng

被引：57
|
作者：
Andrews, George E. [1 ]
Merca, Mircea [2 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] Acad Romanian Scientists, Splaiul Independentei 54, Bucharest 050094, Romania
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2018年 / 154卷
关键词：
Partitions; Euler's pentagonal number theorem; Theta series; ALLIED IDENTITIES; 2; THEOREMS; GAUSS;
D O I：
10.1016/j.jcta.2017.10.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide partition-theoretic interpretation of two truncated identities of Gauss solving a problem by Guo and Zeng. We also reveal that these results, together with our previous truncation of Euler's pentagonal number theorem, are essentially corollaries of the Rogers-Fine identity. Finally we examine further positivity questions related to the partition function. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：610 / 619
页数：10
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