For more information about this meeting, contact Robert Vaughan.
| Title: | Almost-primes represented by irreducible polynomials |
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| Seminar: | Algebra and Number Theory Seminar |
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| Speaker: | Robert Oliver, University of Wisconsin |
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| Abstract: |
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| 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 |
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| Date: | 11 / 18 / 2010 |
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| Time: | 11:15am - 12:05pm |
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