The exceptional set for the number of primes in short intervals

Authors
Bazzanella, D Perelli, A
Citation
D. Bazzanella et A. Perelli, The exceptional set for the number of primes in short intervals, J NUMBER TH, 80(1), 2000, pp. 109-124
Citations number
16
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF NUMBER THEORY
ISSN journal
0022314X → ACNP
Volume
80
Issue
1
Year of publication
2000
Pages
109 - 124
Database
ISI
SICI code
0022-314X(200001)80:1<109:TESFTN>2.0.ZU;2-G
Abstract
We investigate the exceptional set E-delta(X, h) associated with the asympt otic formula for the number of primes in short intervals; see Section 1 for the definition. We first obtain two results about the basic structure of t his set, proving the inertia and decrease properties; see Theorem 1. Then w e turn to estimates For the size of E-delta(X, h), showing that non-trivial bounds for \E-delta(X,h)\ can be obtained when h(x) = x(theta) and 1/6 < t heta < 7/12; see Theorem 2. (C) 2000 Academic Press.