Journal of the
Korean Mathematical Society JKMS

The zero-distribution of the Fourier integral $$\int_{-\infty}^{\infty}Q(u)e^{P(u)+izu}du,$$ where $P$ is a polynomial with leading term $-u^{2m}$ ($m\geq 1$) and $Q$ an arbitrary polynomial, is described. To this end, an asymptotic formula for the integral is established by applying the saddle point method.

Keywords: saddle point method, zeros of Fourier integrals

MSC numbers: 30C15, 30D10, 30E15, 42A38