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The Exceptional Set for the Number of Primes in Short Intervals

✍ Scribed by D Bazzanella; A Perelli

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 137 KB
Volume: 80
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2429

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✦ Synopsis

We investigate the exceptional set E $ (X, h) associated with the asymptotic 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 this set, proving the inertia and decrease properties; see Theorem 1. Then we turn to estimates for the size of E $ (X, h), showing that non-trivial bounds for |E $ (X, h)| can be obtained when h(x)=x % and 1Â6<%<7Â12; see Theorem 2.

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