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We re-examine Shatalov-Sternin's proof of existence of resurgent solutions ofa linear ODE. In particular, we take a closer look at the "Riemann surface"(actually, a two-dimensional complex manifold) whose existence, endlesscontinuability and other properties are claimed by those authors. We present adetailed argument for a part of the "Riemann surface" most relevant for theexact WKB method.

Shatalov-Sternin's construction of complex WKB solutions and the associated Riemann surface