Pretentious multiplicative functions and an inequality for the   zeta-function
  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. 
Andrew Granville and K. Soundararajan