Pretentious multiplicative functions and an inequality for the zeta-function

Details Pretentious multiplicative functions and an inequality for the zeta-function Pretentious multiplicative functions and an inequality for the zeta-function

2006-08-16

arxiv.org/abs/math/0608407v1

Mathematics

Number Theory

8 pages

Scientific paper

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.

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