Pretentious multiplicative functions and an inequality for the zeta-function
Number Theory
2007-05-23 v1 Classical Analysis and ODEs
Abstract
We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions that pretend to be another multiplicative function . We formalize a `distance' which gives a measure of such {\sl pretentiousness}, and as one consequence obtain a curious inequality for the zeta-function.
Cite
@article{arxiv.math/0608407,
title = {Pretentious multiplicative functions and an inequality for the zeta-function},
author = {Andrew Granville and K. Soundararajan},
journal= {arXiv preprint arXiv:math/0608407},
year = {2007}
}
Comments
8 pages