Pretentious multiplicative functions and an inequality for the zeta-function

2006/08/16 by Andrew Granville, K. Soundararajan, Granville, Andrew +1
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0608407

openalex publication_date 2006/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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