Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Li, Darren
Institution: Tsinghua University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214319049