Shifted convolution sums of divisor functions with Fourier coefficients

Pub Date : 2024-03-20 DOI:10.1016/j.jnt.2024.02.014
Miao Lou
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Abstract

Let f(z) be a holomorphic cusp form of weight κ for the full modular group SL2(Z). Denote its n-th normalized Fourier coefficient by λf(n). Let τk(n) denote that k-th divisor function with k4. In this paper, we consider the shifted convolution sumnXτk(n)λf(n+h). We succeed in obtaining a non-trivial upper bound, which is uniform in the shift parameter h.

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有傅里叶系数的除数函数的移位卷积和
设 f(z) 是全模态群 SL2(Z) 权重为 κ 的全形尖顶形式。用 λf(n) 表示其 n 次归一化傅里叶系数。让 τk(n) 表示 k≥4 的第 k 个除数函数。本文考虑的是移位卷积和∑n≤Xτk(n)λf(n+h)。我们成功地得到了一个非微妙的上界,它与移位参数 h 一致。
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