Computing the Mertens function on a GPU

2011/07/31 by Eugene Kuznetsov, Kuznetsov, Eugene · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Neural Networks and Applications #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1108.0135

arxiv created 2011/07/31 · openalex publication_date 2011/07/31 · arxiv updated 2011/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A GPU implementation of an algorithm to compute the Mertens function in O(x2/3+\ko) time is discussed. Results for x up to 10²², and a new extreme value for M(x)/x^1/2, -0.585768 (M(x) ≈ -1.996 ∗ 10⁹ at x ≈ 1.161 ∗ 10¹⁹), are reported.An approximate algorithm is used to examine values of M(x) for x up to exp(10¹⁵).

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