We prove that the existence of isolated solutions of systems of equations of analytical functions on compact real domains in Rp, is equivalent to the convergence of the phase of a suitable complex valued integral I(h) for h→∞. As an application, we then use this result to prove that the problem of establishing the irrationality of the value of an analytic function F(x) at a point x0 can be rephrased in terms of a similar phase convergence.
D. Napoletani, D.C. Struppa, The stationary phase method for real analytic geometry, J. Math. Anal. Appl. (2016), http://dx.doi.org/10.1016/j.jmaa.2015.12.047
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