Pretentious multiplicative functions and an inequality for the zeta-function

Abstract

We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions $f$ that pretend to be another multiplicative function $g$. We formalize a `distance' which gives a measure of such {\sl pretentiousness}, and as one consequence obtain a curious inequality for the zeta-function.

Locations

• CRM proceedings & lecture notes - View - PDF
• arXiv (Cornell University) - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF