Let \(\lambda _{f}(n)\) be the normalized Fourier coefficients of a holomorphic Hecke cusp form of full level. We study a generalized divisor problem with \(\lambda _{f}(n)\) over some special sequences. More precisely, for any fixed integer \(k\ge 2\) and \(j\in \{1,2,3,4\},\) we are interested in the following sums$$\begin{aligned} S_{k}(x,j):=\sum _{n\le x}\lambda _{k,f}(n^{j})=\sum _{n\le x}\sum _{n=n_{1}n_{2}\cdots n_{k}}\lambda _{f}(n_{1}^{j})\lambda _{f}(n_{2}^{j})\cdots \lambda _{f}(n_{k}^{j}). \end{aligned}$$

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关于与尖点形式有关的除数问题的一些结果

令\（\ lambda _ {f}（n）\）为全能级Hecke尖端形状的规格化Fourier系数。我们在某些特殊序列上使用\（\ lambda _ {f}（n）\）研究广义除数问题。更准确地说，对于任何固定整数\（k \ ge 2 \）和\（j \ in \ {1,2,3,4 \}，\），我们对以下总和$$ \ begin {aligned} S_感兴趣{k}（x，j）：= \ sum _ {n \ le x} \ lambda _ {k，f}（n ^ {j}）= \ sum _ {n \ le x} \ sum _ {n = n_ {1} n_ {2} \ cdots n_ {k}} \ lambda _ {f}（n_ {1} ^ {j}）\ lambda _ {f}（n_ {2} ^ {j}）\ cdots \ lambda _ {f}（n_ {k} ^ {j}）。\ end {aligned} $$