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Higher correlations of divisor sums related to primes III: small gaps between primes

By D. A. Goldston and C. Y. Yildirim


We use divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that, for any η>0, a positive proportion of consecutive primes are within 1/4 + η times the average spacing between primes

Year: 2007
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