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

页码：610 / 619

页数：10

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