扭曲的加法除数问题

Pub Date : 2024-07-17 DOI:10.1016/j.jnt.2024.06.007
Alex Cowan
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引用次数: 0

摘要

我们给出了非零复数 u,v 和非三维 Dirichlet 字符 χ,ψ 的移位卷积形式∑n<Xσ2u(n,χ)σ2v(n+k,ψ)nu+v 的渐近线。我们利用自动正则化技术找到了爱森斯坦数列组合的谱分解,该组合并不明显可平方整定。我们得到的误差项在某些情况下比我们使用的方法通常得到的误差项要小。
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A twisted additive divisor problem

We give asymptotics for shifted convolutions of the formn<Xσ2u(n,χ)σ2v(n+k,ψ)nu+v for nonzero complex numbers u,v and nontrivial Dirichlet characters χ,ψ. We use the technique of automorphic regularization to find the spectral decomposition of a combination of Eisenstein series which is not obviously square-integrable. The error term we obtain is in some cases smaller than what the method we use typically yields.

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