A smoothed GPY sieve

Abstract

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.

Locations

• Bulletin of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
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