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2019•Bulletin of the Australian Mathematical SocietyOpen access

ON LITTLEWOOD’S PROOF OF THE PRIME NUMBER THEOREM

Aleksander Simonič

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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.

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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.

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Available 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.

Key concepts: Multiplicative number theory, Prime number theorem, Mathematics, Equivalence (formal languages), Riemann hypothesis, Prime number, Prime (order theory), Number theory

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