PreprintCC BY 4.0arXiv
Computing the divisor summatory function in N9/28+o(1)
Abstract
We present an analytic algorithm to compute isolated values of the divisor summatory function in N9/28+o(1) expected time, improving upon existing methods that require O(N1/3) 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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BibTeX
@misc{li2026computing,
title = {{Computing the divisor summatory function in $N^9/28+o(1)$}},
author = {Darren Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29949},
eprint = {2609.29949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29949},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Computing the divisor summatory function in N^9/28+o(1)
AU - Darren Li
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29949
UR - https://arxiv.org/abs/2609.29949
AB - 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.
ER -