ON LITTLEWOOD’S PROOF OF THE PRIME NUMBER THEOREM

Aleksander Simonič

Type: Article

Publication Date: 2019-08-15

Citations: 1

DOI: https://doi.org/10.1017/s0004972719000881

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.

Locations

Bulletin of the Australian Mathematical Society - View
arXiv (Cornell University) - View - PDF

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Works That Cite This (1)

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+ PDF Chat	NEW EFFECTIVE RESULTS IN THE THEORY OF THE RIEMANN ZETA-FUNCTION	2023	Aleksander Simonič

Works Cited by This (11)

Action	Title	Year	Authors
+	Almost periodic functions	1968	C. Corduneanu N. Gheorghiu
+ PDF Chat	The Distribution of Prime Numbers	1933	A. E. Ingham
+	Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work	1978	G. H. Hardy
+ PDF Chat	Almost Periodic Functions	1933	A. S. Besicovitch
+	The distribution of prime numbers	1990	A. A. Karatsuba
+ PDF Chat	Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes	1916	G. H. Hardy J. E. Littlewood
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown
+ PDF Chat	Note on function spaces with the topology of pointwise convergence	2003	Jan van Mill Jan Pelant Roman Pol
+	Almost periodic functions	1955	J. D. Weston
+	Almost periodic functions	1990	А. А. Панков