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Pretentious multiplicative functions and an inequality for the zeta-function

Andrew Granville·K. Soundararajan
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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.

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Andrew Granville, K. Soundararajan. 2006-08-16. Pretentious multiplicative functions and an inequality for the zeta-function. https://arxiv.org/abs/math/0608407

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