2017/07/29 by Pentti Haukkanen, László Tóth, Haukkanen, Pentti +1 · 1 citation
Computer Science · Mathematics · #11N37 #15B36 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Primary 11C20 #secondary 11A25
paper · pdf · doi:10.48550/arxiv.1707.09473
openalex publication_date 2017/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S=\x1,x2,…,xn\ be a set of distinct positive integers, and let f be an arithmetical function. The GCD matrix (S)f on S associated with f is defined as the n× n matrix having f evaluated at the greatest common divisor of xi and xj as its ij entry. The LCM matrix [S]f is defined similarly. We consider inertia, positive definiteness and ℓp norm of GCD and LCM matrices and their unitary analogs. Proofs are based on matrix factorizations and convolutions of arithmetical functions.