An improvement on the parity of Schur's partition function
An improvement on the parity of Schur's partition function
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DOI：
10.1016/j.jmaa.2023.127530
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发表时间：
2022-11
影响因子：
1.3
通讯作者：
Yiwen Lu;Tao Wei;Xuejun Guo
中科院分区：
文献类型：
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作者：
Yiwen Lu;Tao Wei;Xuejun Guo
摘要对s - c进行了改进。Chen关于Schur配分函数奇偶性的结果。设A (n)为n的Schur划分的个数，即n被划分为等于1,2 （mod 3）的不同部分的个数。研究所。陈[3]显示x (log x) 47 48≪♯{0≤n≤x: A （2n + 1）是奇数}≪x (log x) 12。在本文中，我们将Chen的结果改进为x (log log x) 11 12≪♯{0≤n≤x: A （2n + 1）是奇数}≪x (log x) 12。
Abstract We improve S.-C. Chen's result on the parity of Schur's partition function. Let A (n) be the number of Schur's partitions of n, ie, the number of partitions of n into distinct parts congruent to 1, 2 (mod 3). S.-C. Chen [3] shows x (log x) 47 48≪♯{0≤ n≤ x: A (2 n+ 1) is odd}≪ x (log x) 1 2. In this paper, we improve Chen's result to x (log x) 11 12≪♯{0≤ n≤ x: A (2 n+ 1) is odd}≪ x (log x) 1 2.