## Almost-primes represented by quadratic polynomials

- Date: 03/01/2007

Lecturer(s):

Vishaal Kapoor (University of British Columbia)

Location:

University of British Columbia

Topic:

Dirichlet's theorem on primes in arithmetic progressions characterizes

those linear polynomials which take on prime values infinitely often.

However, this is where the current state of knowledge ends. For the

case of polynomials with higher degrees, heuristic arguments lead us to

believe that for an irreducible polynomial with integer coefficients,

if the leading coefficient is positive and the polynomial has no fixed

prime divisor, then the polynomial represents primes infinitely often.

I will discuss the case for quadratic polynomials with an emphasis on

the work of Iwaniec.

Other Information:

SFU/UBC Number Theory Seminar 2007