In their study of the truncation of Euler's pentagonal number theorem, Andrews and Merca introduced a partition function to count the number of partitions of in which is the least integer that is not a part and there are more parts exceeding than there are below . In recent years, two conjectures concerning on truncated theta series were posed by Andrews, Merca, and Yee. In this paper, we prove that the two conjectures are true for sufficiently large whenever is fixed.

中文翻译：

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Andrews、Merca 和 Yee 关于截断 theta 级数的两个猜想

Andrews和Merca在研究欧拉五边形数定理的截断时，引入了一个配分函数来统计其中不是部分的最小整数且超出的部分多于下面的部分的数量。近年来，Andrews、Merca 和 Yee 提出了两个关于截断 theta 级数的猜想。在本文中，我们证明只要 足够大，这两个猜想都是正确的。