@MISC{Goldston_smallgaps, author = {D. A. Goldston and C. Y. Yildirim}, title = {Small gaps between primes}, year = {} }

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Abstract

ABSTRACT. We use short 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 + η times the average spacing between primes. 4 1.