2023/03/02 by Tsz Ho Chan, Chan, Tsz Ho
Computer Science · Mathematics · #Analytic Number Theory Research #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2303.01168
openalex publication_date 2023/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Roughly speaking, the spectrum of multiplicative functions is the set of all possible mean values. In this paper, we are interested in the spectra of multiplicative functions supported over powerful numbers. We prove that its real logarithmic spectrum takes values from - √(2) / (4 + √(2)) = -0.26160... to 1 while it is known that the logarithmic spectrum of real multiplicative functions over all natural numbers takes values from 0 to 1. In the course of this study, we correct a proof of Granville and Soundararajan concerning contribution of small primes in the study of mean value of multiplicative functions.