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arXiv · 1808.02583

Dirichlet divisor problem on Gaussian integers

Andrew V. Lelechenko
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Abstract

We improve existing estimates of moments of the Riemann zeta function. As a consequence, we are able to derive new estimates for the asymptotic behaviour of $\sum_{N \alpha \le x} \mathfrak{t}_k(\alpha)$, where $N$ stands for the norm of a complex number and $\mathfrak{t}_k$ is the $k$-dimensional divisor function on Gaussian integers.

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Andrew V. Lelechenko. 2018-08-07. Dirichlet divisor problem on Gaussian integers. https://arxiv.org/abs/1808.02583

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