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|YU-RU LIU, Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138-2901, USA|
|The Turán sieve and probabilistic Galois theory|
We introduce the Turán sieve and apply it to the probabilistic Galois theory problem in both the rational and the functional cases. More precisely, we estimate the number of polynomials of degree nand height whose Galois group is a proper subgroup of Sn.