Overpartitions and ternary quadratic forms

详细信息    查看全文

• 作者：Xinhua Xiong
• 关键词：Ternary quadratic forms ; Overpartition ; Congruences
• 刊名：The Ramanujan Journal
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：42
• 期：2
• 页码：429-442
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Number Theory; Field Theory and Polynomials; Combinatorics; Fourier Analysis; Functions of a Complex Variable;
• 出版者：Springer US
• ISSN：1572-9303
• 卷排序：42

文摘

Let \(\overline{p}(n)\) denote the number of overpartitions of n. Recently, Mahlburg showed that \(\overline{p}(n) \equiv 0 \pmod {64}\) and Kim showed that \(\overline{p}(n) \equiv 0 \pmod {128}\) for almost all integers n. In this paper, with the help of some ternary quadratic forms, we prove that \(\overline{p}(n) \equiv 0 \pmod {256}\) for almost all integers n, which was conjectured by Mahlburg.