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.

Location: http://mech.math.msu.su/~fpm/eng/k10/k105/k10502h.htm

Last modified: May 30, 2011