This article is cited in 2 papers

Multiplicity and vanishing lemmas for differential and $q$-difference equations in the Siegel–Shidlovsky theory

D. Bertrand

Université Pierre & Marie Curie, Paris VI, France

Abstract: We present a general multiplicity estimate for linear forms in solutions of various types of functional equations, which extends the zero estimates used in some recent works on the Siegel–Shidlovsky theorem and its $q$-analogues. We also present a dual version of this estimate, as well as a new interpretation of Siegel's theorem itself in terms of periods of Deligne's irregular Hodge theory.

UDC: 511.46+512.628

 English version: Journal of Mathematical Sciences (New York), 2012, 180:5, 542–549

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