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ON LITTLEWOOD’S PROOF OF THE PRIME NUMBER THEOREM

Part of: Multiplicative number theory Harmonic analysis in one variable

Published online by Cambridge University Press:  15 August 2019

ALEKSANDER SIMONIČ Open the ORCID record for ALEKSANDER SIMONIČ [Opens in a new window]
ALEKSANDER SIMONIČ*
Affiliation:
School of Science, The University of New South Wales (Canberra), ACT, Australia email aleks.simonic@gmail.com
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Abstract

In this note we examine Littlewood’s proof of the prime number theorem. We show that this can be extended to provide an equivalence between the prime number theorem and the nonvanishing of Riemann’s zeta-function on the one-line. Our approach goes through the theory of almost periodic functions and is self-contained.

Keywords

prime number theoremalmost periodic function

MSC classification

Primary: 11N05: Distribution of primes
Secondary: 42A75: Classical almost periodic functions, mean periodic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 226 - 232
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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