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On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class

Abstract:

We establish the equivalence of conjectures concerning the pair correlation of zeros of 𝐿 ‐functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston and Montgomery [‘Pair correlation of zeros and primes in short intervals’, Analytic number theory and Diophantine problems (Stillwater, 1984), Progress in Mathematics 70 (1987) 183–203] and Montgomery and Soundararajan [‘Primes in short...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/jlms/jdw030

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Queens College
Role:
Author
Publisher:
Wiley
Journal:
Journal of the London Mathematical Society More from this journal
Volume:
94
Issue:
1
Pages:
161-185
Publication date:
2016-06-01
Acceptance date:
2016-04-11
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Keywords:
Pubs id:
pubs:1049630
UUID:
uuid:f8513585-6cc8-45a6-9fc5-9e8ac472e500
Local pid:
pubs:1049630
Source identifiers:
1049630
Deposit date:
2019-09-25

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