  We present a comprehensive analysis of the implications of conformal
invariance for 3-point functions of the stress-energy tensor, conserved
currents and scalar operators in general dimension and in momentum space. Our
starting point is a novel and very effective decomposition of tensor
correlators which reduces their computation to that of a number of scalar form
factors. For example, the most general 3-point function of a conserved and
traceless stress-energy tensor is determined by only five form factors.
Dilatations and special conformal Ward identities then impose additional
conditions on these form factors. The special conformal Ward identities become
a set of first and second order differential equations, whose general solution
is given in terms of integrals involving a product of three Bessel functions
(`triple-K integrals'). All in all, the correlators are completely determined
up to a number of constants, in agreement with well-known position space
results. We develop systematic methods for explicitly evaluating the triple-K
integrals. In odd dimensions they are given in terms of elementary functions
while in even dimensions the results involve dilogarithms. In some cases, the
triple-K integrals diverge and subtractions are necessary and we show how such
subtractions are related to conformal anomalies.
  This paper contains two parts that can be read independently of each other.
In the first part, we explain the method that leads to the solution for the
correlators in terms of triple-K integrals and how to evaluate these integrals,
while the second part contains a self-contained presentation of all results.
Readers interested only in results may directly consult the second part of the
paper.
