标题： 克兰克等分布和$(k,j)$-带划线分拆 显示英文标题

标题： Crank equidistribution and $(k,j)$-overlined partitions

摘要： 在2023年发表的一篇论文中，Wagner引入并研究了具有复乘的雅可比形式，并给出了几个应用。 其中一个应用是构造了一类新的双无限的分拆理论对象，称为$(k,j)$-色超分拆，并由$\overline{p}_{k,j}$标记，利用雅可比形式构造了解释$\overline{p}_{k,j}$所满足的拉马努金型同余关系的挠函数。 在本说明中，我们给出了$(k,j)$-色超分拆数量的渐近公式，并证明了由Wagner构造的任何挠函数在算术序列上渐近均匀分布，这遵循文献中几篇最近的论文。 显示英文摘要

摘要： In a paper published in 2023, Wagner introduced and studied Jacobi forms with complex multiplication, and gave several applications. One such application was in constructing a new doubly-infinite family of partition-theoretic objects, called $(k,j)$-coloured overpartitions and labelled by $\overline{p}_{k,j}$, and using the Jacobi forms to construct crank functions which explain the Ramanujan-type congruences satisfied by $\overline{p}_{k,j}$. In this note, we give an asymptotic formula for the number of $(k,j)$-coloured overpartitions and prove that any crank constructed by Wagner is asymptotically equidistributed on arithmetic progressions, following several recent papers in the literature.