# Meeting Details

Title: Almost-primes represented by irreducible polynomials Algebra and Number Theory Seminar Robert Oliver, University of Wisconsin Let G(x) be an irreducible polynomial with integer coefficients. It is conjectured that the set {n \in N: G(n) is prime} is infinite for most G(x). If P_r denotes the set of squarefree positive integers with at most r prime factors, we consider the set {n \in N : G(n)\in P_r} with the goal of showing that it is infinite for a suitable choice of r. Considerable work has been done on this problem, with the most notable results being due to Iwaniec, Buchstab, and Richert. Here we show that if deg(G(x)) = 2, then we may take r=2. For those G(x) with deg(G(x))>= 3, we establish conditions on G(x) which allow us to conclude that there is a suitable choice of r <= deg(G(x)).

### Room Reservation Information

Room Number: MB106 11 / 18 / 2010 11:15am - 12:05pm