J. Korean Math. Soc. 2007; 44(2): 455-466
Printed March 1, 2007
https://doi.org/10.4134/JKMS.2007.44.2.455
Copyright © The Korean Mathematical Society.
Haseo Ki and Young-One Kim
Yonsei University, Seoul National University
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
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