论文标题
改善了Schur分区功能的均衡
An improvement on the parity of Schur's partition function
论文作者
论文摘要
我们改善了S.-C。陈的结果是Schur分区功能的均等。令$ a（n）$是$ n $的舒尔分区的数量，即$ n $的分区数量到不同的零件，一致，$ 1，2 \ mod {3} $。 S.-C。 Chen \ cite {Mr3959837}显示$ \ small \ frac {x} {（\ log {x}}）^{\ frac {47} {48}}}}}} \ ll \ shrow \ shrow \ {0 \ le n \ le n \ le x：a（2n+1） \ text {是奇数} \} \ ll \ frac {x} {（\ log {x}}）^{\ frac {1} {2}}}} $。在本文中，我们将Chen的结果提高到$ \ frac {x} {（\ log {x}）^{\ frac {\ frac {11} {12}}}} \ ll \ sharp \ sharp \ {0 \ le n \ le n \ le n \ le x：a（2n+1）\ \ \; \ text {是奇数} \} \ ll \ frac {x} {（\ log {x}）^{\ frac {1} {2}}}}}}
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 $n$, i.e., the number of partitions of $n$ into distinct parts congruent to $1, 2 \mod{3}$. S.-C. Chen \cite{MR3959837} shows $\small \frac{x}{(\log{x})^{\frac{47}{48}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}$. In this paper, we improve Chen's result to $\frac{x}{(\log{x})^{\frac{11}{12}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}.$
