Truncated theta series and a problem of Guo and Zeng

被引：65

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

共 13 条

[1] 2 THEOREMS OF GAUSS AND ALLIED IDENTITIES PROVED ARITHMETICALLY [J].

ANDREWS, GE .

PACIFIC JOURNAL OF MATHEMATICS, 1972, 41 (03) :563-&

[2] The truncated pentagonal number theorem [J].

Andrews, George E. ;

Merca, Mircea .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (08) :1639-1643

[3]

[Anonymous], 1998, THEORY PARTITIONS

[4] Truncated series from the quintuple product identity [J].

Chan, Song Heng ;

Ho, Thi Phuong Nhi ;

Mao, Renrong .

JOURNAL OF NUMBER THEORY, 2016, 169 :420-438

[5] Overpartitions [J].

Corteel, S ;

Lovejoy, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (04) :1623-1635

[6]

Fine NJ, 1988, BASIC HYPERGEOMETRIC SERIES AND APPLICATIONS

[7] Two truncated identities of Gauss [J].

Guo, Victor J. W. ;

Zeng, Jiang .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2013, 120 (03) :700-707

[8] Bilateral truncated Jacobi's identity [J].

He, Thomas Y. ;

Ji, Kathy Q. ;

Zang, Wenston J. T. .

EUROPEAN JOURNAL OF COMBINATORICS, 2016, 51 :255-267

[9] Another approach to the Truncated Pentagonal Number Theorem [J].

Kolitsch, Louis W. .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2015, 11 (05) :1563-1569

[10] Proofs of two conjectures on truncated series [J].

Mao, Renrong .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2015, 130 :15-25

← 1 2 →