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October, 1978 A Log Log Improvement to the Riemann Hypothesis for the Hawkins Random Sieve
C. C. Heyde
Ann. Probab. 6(5): 870-875 (October, 1978). DOI: 10.1214/aop/1176995433

Abstract

This paper is concerned with the Hawkins random sieve which is a probabilistic analogue of the sieve of Eratosthenes. Analogues of the prime number theorem, Mertens' theorem and the Riemann hypothesis have previously been established for the Hawkins sieve. In the present paper we give a more delicate analysis using iterated logarithm results for both martingales and tail sums of martingale differences to deduce a considerably improved $\log\log$ replacement for the Riemann hypothesis result.

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C. C. Heyde. "A Log Log Improvement to the Riemann Hypothesis for the Hawkins Random Sieve." Ann. Probab. 6 (5) 870 - 875, October, 1978. https://doi.org/10.1214/aop/1176995433

Information

Published: October, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0414.60032
MathSciNet: MR503956
Digital Object Identifier: 10.1214/aop/1176995433

Subjects:
Primary: 60F15
Secondary: 10H30, 60G45, 60J05

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • October, 1978
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