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Sifting short intervals II

Published online by Cambridge University Press:  24 October 2008

John B. Friedlander
John B. Friedlander
Affiliation:
University of Toronto
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Extract

Let g(y) denote an arbitrary real-valued function satisfying g(y) → ∞ as y → ∞. One expects, and, subject to certain conjectures, Heath-Brown(3) has proved, that for all y in (1, X], apart from a set of measure o(X), the interval (y, y + g(y) log y] contains primes.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 3 , November 1982 , pp. 381 - 384
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Friedlander, J. B.Sifting short intervals. Math. Proc. Cambridge Phil. Soc. 91 (1982), 9–15.CrossRefGoogle Scholar
(2)Friedlander, J. B.Large prime factors in small intervals. Colloq. Math. Soc. Janos Bolyai 34 (to appear).Google Scholar
(3)Heath-Brown, D. R.Gaps between primes, and the pair correlation of zeros of the zeta-function. Acta Arith. (to appear).Google Scholar
(4)Iwaniec, H.Rosser's sieve. Acta Arith. 36 (1980), 171–202.CrossRefGoogle Scholar