Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

The Turan Sieve Method and Some of Its Applications


Affiliations
1 Department of Mathematics, Harvard University Cambridge, Mass., 02138, United States
2 Department of Mathematics and Statistics, Queen's University, Kingston Ontario, K7L 3N6, Canada
     

   Subscribe/Renew Journal


We introduce the Turan sieve method and apply it to the probabilistic Galois theory problems in both the rational number field and the function field cases. We estimate the number of polynomials of degree n and height ≤ N whose Galois group is a proper subgroup of Sn- For the rational number field case, we get an estimate of O(Nn-1/3(logN)<sup.2) and in the case of the function field over Fq, we get O(Nn-1logqN).
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 249

PDF Views: 0




  • The Turan Sieve Method and Some of Its Applications

Abstract Views: 249  |  PDF Views: 0

Authors

Yu-Ru Liu
Department of Mathematics, Harvard University Cambridge, Mass., 02138, United States
M. Ram Murty
Department of Mathematics and Statistics, Queen's University, Kingston Ontario, K7L 3N6, Canada

Abstract


We introduce the Turan sieve method and apply it to the probabilistic Galois theory problems in both the rational number field and the function field cases. We estimate the number of polynomials of degree n and height ≤ N whose Galois group is a proper subgroup of Sn- For the rational number field case, we get an estimate of O(Nn-1/3(logN)<sup.2) and in the case of the function field over Fq, we get O(Nn-1logqN).