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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.


NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications in 2015. DOI: 10.1016/j.jmaa.2015.12.047

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