Elementary integrals and the resolution of singularities of the phase
Vladimir I. Arnold, Sabir Medzhidovich Gusein-Zade, Alexander N. Varchenko · Birkhäuser Boston eBooks · 2012
In this chapter we shall study the asymptotics ofan oscillatory integral, the phase of which is a monomial. We shall indicate the connection between the asymptotics of an oscillatory integral and the poles of the meromorphic function $$ F(\lambda)= \int f^{\lambda}(x)\phi(x) dx,$$ where f is the phase, and $$\phi$$ is the amplitude of the oscillatory integral.