  Let Pd denote the space of all real polynomials of degree at most d. It is an
old result of Stein and Wainger that for every polynomial P in Pd:
  |p.v.\int_R {e^{iP(t)} dt/t} | < C(d) for some constant C(d) depending only
on d. On the other hand, Carbery, Wainger and Wright claim that the true order
of magnitude of the above principal value integral is log d. We prove this
conjecture.
