MORE PRECISE PAIR CORRELATION OF ZEROS AND PRIMES IN SHORT INTERVALS

Tsz Ho Chan

Type: Article

Publication Date: 2003-11-17

Citations: 13

DOI: https://doi.org/10.1112/s0024610703004769

Abstract

Goldston and Montgomery proved that the strong pair correlation conjecture and two second moments of primes in short intervals are equivalent to each other under the Riemann hypothesis. The paper obtains the second main terms for each of the above, and it is shown that they are almost equivalent to each other.

Locations

Journal of the London Mathematical Society - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (5)

Action	Title	Year	Authors
+	Multiplicative Number Theory	1980	H. Davenport
+	Pair Correlation of Zeros and Primes in Short Intervals	1987	D. A. Goldston Hugh L. Montgomery
+ PDF Chat	On the fractional parts of $x/n$ and related sequences. III	1977	Bahman Saffari R. C. Vaughan
+	Table of Integrals, Series, and Products	1980
+	Beyond pair correlation	2000	Hugh L. Montgomery K. Soundararajan