Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-21T04:10:47.500Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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