On asymptotic behavior for the Hawkins random sieve
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- by C. C. Heyde PDF
- Proc. Amer. Math. Soc. 56 (1976), 277-280 Request permission
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 and Mertens’ theorem have previously been obtained for this sieve by classical probabilistic methods. In the present paper, sharper results akin to the Riemann hypothesis are obtained by a more elegant martingale approach.References
- David Hawkins, The random sieve, Math. Mag. 31 (1957/58), 1–3. MR 99321, DOI 10.2307/3029322
- David Hawkins, Random sieves. II, J. Number Theory 6 (1974), 192–200. MR 345926, DOI 10.1016/0022-314X(74)90013-4 J. Neveu, Cacul des probabilités, 2nd ed., Masson, Paris, 1970.
- David Williams, A study of a diffusion process motivated by the Sieve of Eratosthenes, Bull. London Math. Soc. 6 (1974), 155–164. MR 359027, DOI 10.1112/blms/6.2.155
- M. C. Wunderlich, The prime number theorem for random sequences, J. Number Theory 8 (1976), no. 4, 369–371. MR 429799, DOI 10.1016/0022-314X(76)90084-6
- M. C. Wunderlich, A probabilistic setting for prime number theory, Acta Arith. 26 (1974/75), 59–81. MR 371834, DOI 10.4064/aa-26-1-59-81
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 277-280
- MSC: Primary 10H30
- DOI: https://doi.org/10.1090/S0002-9939-1976-0404177-X
- MathSciNet review: 0404177