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A smoothed GPY sieve
Author(s) -
Motohashi Yoichi,
Pintz János
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn023
Subject(s) - mathematics , preprint , twin prime , sieve (category theory) , extension (predicate logic) , prime number theorem , conjecture , number theory , discrete mathematics , pure mathematics , bounded function , prime (order theory) , combinatorics , prime number , mathematical analysis , computer science , world wide web , programming language
Combining the arguments developed in the works of D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yildirim [Preprint, 2005, arXiv: math.NT/506067] and Y. Motohashi [ Number theory in progress – A. Schinzel Festschrift (de Gruyter, 1999) 1053–1064] we introduce a smoothing device to the sieve procedure of Goldston, Pintz, and Yildirim (see [ Proc. Japan Acad. 82A (2006) 61–65] for its simplified version). Our assertions embodied in Lemmas 3 and 4 of this article imply that a natural extension of a prime number theorem of E. Bombieri, J. B. Friedlander, and H. Iwaniec [Theorem 8 in Acta Math. 156 (1986) 203–251] should give rise infinitely often to bounded differences between primes, that is, a weaker form of the twin prime conjecture.

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