We study the divisibility properties of the partition function associated with the eighth-order mock theta function \(V_0(q)\), introduced by Gordon and McIntosh. We obtain congruences modulo powers of 2 for certain coefficients of the partition function, akin to Ramanujan’s partition congruences. Further, we also present several infinite families of congruences modulo 13, 25, and 27.

中文翻译：

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八阶模拟θ函数$$ V_0（q）$$ V 0（q）的系数的同余性质

我们研究了由Gordon和McIntosh引入的与八阶模拟theta函数\（V_0（q）\）相关的分区函数的可除性。对于分配函数的某些系数，我们获得2的模余幂，类似于Ramanujan的分区同余。此外，我们还提出了数模13、25和27的无限个同余族。