Number Theory Working Seminar
Abel Castillo
University of Illinois at Chicago
Probabilistic Galois Theory - Gallagher's Theorem
Abstract: Let n be an integer and H > 0. In 1936, van der Waerden conjectured that the number of
monic, degree n polynomials with coefficients in Z, height at most H and Galois group strictly embedded in S_n
is $O(H^{n-1})$. Using a multidimensional large sieve inequality, in 1972 Gallagher proved the bound $O(H^{n- 1/2} \log H)$.
We will discuss this classical result and its generalizations to other arithmetic contexts.
Wednesday February 6, 2013 at 9:30 AM in SEO 512