A note on the number of primes in short intervals

Authors:
D. A. Goldston and S. M. Gonek

Journal:
Proc. Amer. Math. Soc. **108** (1990), 613-620

MSC:
Primary 11N05

DOI:
https://doi.org/10.1090/S0002-9939-1990-1002158-6

MathSciNet review:
1002158

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , where the sum is over prime powers. H. L. Montgomery has shown that on the Riemann hypothesis, there is a positive constant such that for each , provided that is sufficiently large. Here we prove a slightly stronger result from which we deduce a lower bound of the same order.

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1002158-6

Article copyright:
© Copyright 1990
American Mathematical Society