FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 5, PAGES 19-30

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

D. Bertrand

Abstract

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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.

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Last modified: May 30, 2011