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The average size of gaps between primes

Published online by Cambridge University Press:  26 February 2010

Carlos Julio Moreno
Carlos Julio Moreno
Affiliation:
Department of Mathematics, University of IllinoisUrbana, Illinois, U.S.A.
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Extract

Erdoső has asked whether there exists a positive constant c < 1 such that

where pn is the n-th prime. In 1943 Selberg «3» proved, on the assumption of the Riemann Hypothesis, that

uniformly for H > 0. By an elementary extension of Selberg's method we prove the following two results free of any unproved assumptions.

Type
Research Article
Information
Mathematika , Volume 21 , Issue 1 , June 1974 , pp. 96 - 100
Copyright
Copyright © University College London 1974

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References

1.Chandrasekharan, K.. Arithmetical functions (Springer- Verlag, New York, 1970).CrossRefGoogle Scholar
2.Montgomery, H.. “Zeros of L-functions”, Inventiones math., 8 (1969), 346–354.CrossRefGoogle Scholar
3.Selberg, A.. “On the normal density of primes in short intervals and the difference between consecutive primes”, Arch. Math. Naturvid., 47, No. 6 (1943), 1–19.Google Scholar
4.Walfisz, A.. Weylsche Exponentialsummen in der neueren Zahlentheorie (VEB Deutcher-Verlag der Wis. Berlin, 1963).Google Scholar