On the difference between consecutive primes

@article{Huxley1971OnTD,
  title={On the difference between consecutive primes},
  author={Martin N. Huxley},
  journal={Inventiones mathematicae},
  year={1971},
  volume={15},
  pages={164-170}
}
  • M. Huxley
  • Published 1 June 1971
  • Chemistry
  • Inventiones mathematicae
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References

SHOWING 1-5 OF 5 REFERENCES
On the difference between consecutive primes
[Received 3 August 1937] 1. LET pn denote the nth. prime, and 77(2;) the number of primes p not exceeding x. The existence of an absolute constant 6 < 1 such that a (1) n(x) ~ . log a; when x -> 00,
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
Zeros ofL-functions
for some fixed A and B. Both (2) and (3) are proved by the use of mean value theorems, the large sieve in the case of (3). The lack of a bound for (1) which is good with respect to both Q and Tmay be