Globally bounded solutions of differential equations

The aim of this paper is to give an account of some results and conjectures involving “for almost all p” properties of power series. Our main concern is to exhibit links between three topics : automaticity, algebraicity (mod n) and D-finiteness. Diagonals of rational fractions seem to be at the hear...

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Bibliographic Details
Published inAnalytic Number Theory pp. 45 - 64
Main Author Gilles, Christol
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 22.10.2006
SeriesLecture Notes in Mathematics
Subjects
Algebraic Function
Differential Module
Hypergeometric Function
Mixed Hodge Structure
Rational Fraction
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ISBN9783540527879
3540527877
ISSN0075-8434
1617-9692
DOI10.1007/BFb0097124

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Summary:The aim of this paper is to give an account of some results and conjectures involving “for almost all p” properties of power series. Our main concern is to exhibit links between three topics : automaticity, algebraicity (mod n) and D-finiteness. Diagonals of rational fractions seem to be at the heart of the problem. In the last part, we show they appear as (regular) solutions near singularity of Picard-Fuchs differential equations.
ISBN:9783540527879
3540527877
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0097124