Asymptotic Sieve for Primes

Abstract

For a long time it was believed that sieve methods might be incapable of achieving the goal for which they had been created, the detection of prime numbers. Indeed, it was shown [S], [B] to be inevitable that, in the sieve’s original framework, no such result was possible although one could come tantalizingly close. This general limitation is recognized as the \parity problem of sieve theory. More recently, beginning with the work [IJ], this goal has in certain cases become possible by adapting the sieve machinery to enable it to take advantage of the input of additional analytic data. There have been a number of recent developments in this regard, for example [H], [DFI], [FI], and several recent works of R.C. Baker and G. Harman. The story however is far from flnished. In this paper we consider a sequence of real nonnegative numbers

Locations

• arXiv (Cornell University) - PDF
• Annals of Mathematics - View