Arithmetic properties of bipartitions with designated summands

被引：3
|
作者：
Naika M.S.M. [1 ]
Shivashankar C. [1 ]
机构：
[1] Department of Mathematics, Bangalore University, Central College Campus, Bangalore, 560 001, Karnataka
来源：
Boletín de la Sociedad Matemática Mexicana | 2018年 / 24卷 / 1期
关键词：
Bipartitions with designated summands; Congruences; Theta function;
D O I：
10.1007/s40590-016-0140-8
中图分类号：
学科分类号：
摘要：
In 2002 Andrews, Lewis and Lovejoy introduced partition function PD(n), the number of partitions of n with designated summands and using modular forms they obtained many congruences modulo 3 and powers of 2. For example, they proved PD(3n+2)≡0(mod3). In this paper, we study various arithmetic properties of PD2(n) modulo 3 and powers of 2, where PD2(n) denotes the number of bipartitions of n with designated summands. We obtain congruences like PD2(3α+3(3n+2))≡0(mod3), PD2(3α+3(6n+4))≡0(mod3), PD2(24n+15)≡0(mod25), PD2(24n+23)≡0(mod25), PD2(24n+12)≡0(mod12) and PD2(18n+15)≡0(mod48). © 2016, Sociedad Matemática Mexicana.
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页码：37 / 60
页数：23
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