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arXiv · 2609.29949

Computing the divisor summatory function in $N^{9/28+o(1)}$

Darren Li
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Abstract

We present an analytic algorithm to compute isolated values of the divisor summatory function in $N^{9/28+o(1)}$ expected time, improving upon existing methods that require $O(N^{1/3})$ time. Our method significantly departs from elementary approaches to analyze the geometry of the Dirichlet hyperbola, relying instead on Voronoï summation and accelerating the evaluation of the resulting exponential sum.

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Darren Li. 2026-09-24. Computing the divisor summatory function in $N^{9/28+o(1)}$. https://arxiv.org/abs/2609.29949

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