On the Asymptotics and Zeros of a Class of Fourier Integrals

We obtain the asymptotic expansion of the Fourier integrals Z ∞ 0 t ν−1 cos sin (x t) exp (−t n /n) d t 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.