The spectrum of multiplicative functions
数论
2016-09-07 v1
摘要
Let S be a subset of the unit disk, and let F(s) denote the class of completely multiplicative functions f such that f(p) is in S for all primes p. The authors' main concern is which numbers arise as mean-values of functions in F(s). More precisely, let Gamma_N(S) = {1/N sum_{n <= N} f(n): f in F(S)} and Gamma(S) = lim_{N -> infinity} Gamma_N(s). The authors call Gamma(S) the spectrum of the set S, and study its properties.
引用
@article{arxiv.math/9909190,
title = {The spectrum of multiplicative functions},
author = {Andrew Granville and K. Soundararajan},
journal= {arXiv preprint arXiv:math/9909190},
year = {2016}
}
备注
Abstract added in migration