Journal of the Ramanujan Mathematical Society

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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
     

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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).
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  • The Turan Sieve Method and Some of Its Applications

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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).