Reference Database (references for the Prime Pages)

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This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

#### Item(s) in original BibTeX format

@article{BH96,
author={R. C. Baker and G. Harman},
title={The difference between consecutive primes},
abstract={The main result of the paper is that for all large $x$, the interval $A=[x-x^{0.535},x]$
contains prime numbers. The most recent published result meeting rigorous
standards is due to Iwaniec and Pintz ($0.547\dots$ in place of $0.535$).
The idea is to begin with asymptotic formulas for sums over products such
as $pqm$ in $A$ where $p$ and $q$ run over primes in suitably restricted
intervals and $m$ over some set of integers. One then builds on these formulae
using the sieve method of Harman (On the distribution of $\alpha p$ modulo
one' J. London Math. Soc. 27 (1983), 9--18), to obtain asymptotic formula
for sums of the type $$\sum_m \sum_n a_m b_n S(A_{mn}, z),$$ the number
$z$ being a positive power of $x$ depending on the size of $m$ and $n$.
From this point, the use of Buchstab's identity enables one to reach a
lower bound for the number of primes in $A$ of $c$ times the expected value.
Certain integrals in two and four dimensions must be bounded above, using
a computer calculation, in order to ensure a positive value of $c$.},
journal= plms,
volume= 72,
year= 1996,
pages={261--280},
mrnumber={96k:11111},
series= 3
}

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 Another prime page by Chris K. Caldwell