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arXiv · 1506.02608

The Shifted Convolution of Divisor Functions

Berke Topacogullari
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Abstract

We prove an asymptotic formula for the shifted convolution of the divisor functions $d_3(n)$ and $d(n)$, which is uniform in the shift parameter and which has a power-saving error term. The method is also applied to give analogous estimates for the shifted convolution of $d_3(n)$ and Fourier coefficents of holomorphic cusp forms. These asymptotics improve previous results obtained by several different authors.

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Berke Topacogullari. 2015-06-08. The Shifted Convolution of Divisor Functions. https://doi.org/10.1093/qmath/haw010

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