On the asymptotics and zeros of a class of Fourier integrals (European Journal of Pure and Applied Mathematics, 2012)
We obtain the asymptotic expansion of the Fourier integrals\[\int_0^\infty t^{ u-1}\, \raisebox{-.8ex}{\mbox{$\stackrel{\textstyle\cos}{\sin}$}}\,(xt) \,\exp\,(-t^n/n)\,dt\]for large complex values of $x$ and integer $n>2$ by means of the asymptotic theory of the Wright function. Asymptotic approximations for both the real and complex zeros of these integrals are considered. These results are extended to $p$-dimensional Fourier integrals of a similar structure.