On the sieve parameters alpha Kappa, and beta Kappa, for large Kappa

[摘要] Two parameters, alpha(kappa) and beta(kappa) play a central role in the sieve method of Diamond, Halberstam, and Richert. For each value of the sieve dimension kappa > 1, alpha(kappa) is the point beyond which the DHR upper sieve improves upon the upper bound sieve function of Ankeny and Onishi; and the sieving limit beta(kappa) is the point beyond which the DHR lower sieve yields a nontrivial (i.e., positive) lower bound. We show that for all large enough kappa, alpha(kappa) lies within a bounded distance of rho(kappa), the largest positive zero of Iwaniec's function q(kappa)(.) and that beta(kappa) is smaller than nu(kappa) the sieving limit of the Ankeny-Onishi sieve. (C) 1997 Academic Press.

[发布日期] 1997-11-01