An improvement on the parity of Schur's partition function

2022/11/28 by Lu, Yiwen, Wei, Tao, Guo, Xuejun
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2211.15193

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 \mod3. S.-C. Chen \citeMR3959837 shows \small \fracx(logx)^(47)/(48) ≪ \sharp \0≤ n≤ x:A(2n+1) is odd\≪ \fracx(logx)^(1)/(2). In this paper, we improve Chen's result to \fracx(logx)^(11)/(12) ≪ \sharp \0≤ n≤ x:A(2n+1) is odd\≪ \fracx(logx)^(1)/(2).

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