Almost-primes represented by quadratic polynomials

  • Date: 03/01/2007

Vishaal Kapoor (University of British Columbia)


University of British Columbia


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