Dendromorphic functions
Résumé
We study analytic properties of the Picard-Vessiot closure of ℂ(z). In particular, we show that analytic functions in this closure do not admit natural boundaries in a strong sense. As a consequence, certain differentially algebraic equations over ℂ like the generating series of the partition function do not lie in the Picard-Vessiot closure of ℂ(z).
Domaines
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