Infinite families of arithmetic identities and congruences for bipartitions with 3-cores

被引：8

作者：

Baruah, Nayandeep Deka ^{[1
]}

Nath, Kallol ^{[2
]}

机构：

[1] Tezpur Univ, Dept Math Sci, Sonitpur 784028, Assam, India

[2] Sibsagar Coll, Dept Math, Sivasagar 785665, Assam, India

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 149卷

关键词：

Partitions; t-cores; Bipartitions; Dissections; Theta functions;

D O I：

10.1016/j.jnt.2014.10.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A(3) (n) denote the number of bipartitions of n that are 3-cores. By employing Ramanujan's simple theta function identities, we prove that A(3)(2n + 1) = 1/3 sigma(6n + 5), where sigma(n) denotes the sum of the positive divisors of n. We also find several infinite families of arithmetic identities and congruences for A(3)(n), which include generalizations of some recent results on A(3)(n) by B.L.S. Lin (2014) [6]. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：92 / 104

页数：13

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