Asymptotics and inequalities for partitions into squares

被引：7
|
作者：
Ciolan, Alexandru [1 ]
机构：
[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2020年 / 16卷 / 01期
基金：
欧洲研究理事会;
关键词：
Asymptotics; circle method; partitions; squares;
D O I：
10.1142/S1793042120500074
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of parts. We further show that, for n large enough, the two quantities are different and which of the two is bigger depends on the parity of n. This solves a recent conjecture formulated by Bringmann and Mahlburg (2012).
引用
收藏
页码：121 / 143
页数：23
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