Pretentious multiplicative functions and an inequality for the zeta-function

Andrew Granville; K. Soundararajan

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Pretentious multiplicative functions and an inequality for the zeta-function

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arxiv math/0608407 v1 pith:QEKQMSGC submitted 2006-08-16 math.NT math.CA

Pretentious multiplicative functions and an inequality for the zeta-function

Andrew Granville , K. Soundararajan This is my paper

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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.

Pretentious multiplicative functions and an inequality for the zeta-function

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