Abstract
Let M be a holonomic algebraic D-module on the affine line. Its exponential factors are Puiseux germs describing the growth of holomorphic solutions to M at irregular points. The stationary phase formula states that the exponential factors of the Fourier transform of M are obtained by Legendre transform from the exponential factors of M. We give a microlocal proof of this fact, by translating it in terms of enhanced ind-sheaves through the Riemann–Hilbert correspondence.
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