Recently, Brietzke, Silva and Sellers [‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl.479 (2019), 62–89] studied the number $v_{0}(n)$ of overpartitions of $n$ into odd parts without gaps between the nonoverlined parts, whose generating function is related to the mock theta function $V_{0}(q)$ of order 8. In this paper we first present a short proof of the 3-dissection for the generating function of $v_{0}(2n)$. Then we establish three congruences for $v_{0}(n)$ along certain progressions which are subsequences of the integers $4n+3$.

中文翻译：

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与模拟 THETA 函数相关的过度分区

最近，Brietzke、Silva 和 Sellers ['与 Gordon 和 McIntosh 的八阶模拟 theta 函数相关的同余'，J.数学。肛门。应用程序。479(2019), 62–89] 研究了数字$v_{0}(n)$的过度分区$n$成奇数部分，非上划线部分之间没有间隙，其生成函数与模拟 theta 函数有关$V_{0}(q)$8 阶。在本文中，我们首先给出了生成函数的 3 剖分的简短证明$v_{0}(2n)$. 然后我们建立三个同余$v_{0}(n)$沿着作为整数子序列的某些级数$4n+3$.