preprint · arXiv (Cornell University) · 2022
An improvement on the parity of Schur's partition function
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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 $n$, 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 $\frac{x}{(\log{x})^{\frac{11}{12}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}.$
Cite this paper
Lu, Y., Wei, T., & Guo, X. (2022). An improvement on the parity of Schur's partition function. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2211.15193
Lu, Yiwen, et al. “An improvement on the parity of Schur's partition function.” arXiv (Cornell University), 2022, https://doi.org/10.48550/arxiv.2211.15193.
Lu, Yiwen, Tao Wei, and Xuejun Guo. 2022. “An improvement on the parity of Schur's partition function.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2211.15193.
Lu, Y., Wei, T. and Guo, X. (2022) ‘An improvement on the parity of Schur's partition function’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2211.15193.
@misc{lu2022improvement,
title = {{An improvement on the parity of Schur's partition function}},
author = {Lu, Yiwen and Wei, Tao and Guo, Xuejun},
journal = {arXiv (Cornell University)},
year = {2022},
doi = {10.48550/arxiv.2211.15193}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.