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Arithmetic and Galois Theories of Differential Equations
Edited by: Lucia Di Vizio, Institut de Mathématiques de Jussieu, France, and Tanguy Rivoal, Université Grenoble 1, Saint-Martin d'Héres, France
A publication of the Société Mathématique de France.
Séminaires et Congrès
2011; 405 pp; softcover
Number: 23
ISBN-13: 978-2-85629-331-7
List Price: US$117
Member Price: US$93.60
Order Code: SECO/23
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This volume contains the proceedings of the summer school Galoisian and Arithmetic Theory of Differential Equations, held at the CIRM in Luminy from September 21 to September 25, 2009. This school brought together mathematicians from various areas of research, united by their interest in ordinary differential equations, particularly those that arise in arithmetic.

This volume consists of five surveys, corresponding to the five lecture courses given during the school, plus six original papers, corresponding to research talks also given on this occasion. The volume also contains a reworking, by B. Chiarellotto, G. Gerotto, and F. J. Sullivan, of notes of the lectures on exponential modules given by B. M. Dwork at the University of Padova in 1994.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in arithmetic and Galois theories of differential equations.

Table of Contents

  • D. Bertrand -- Galois descent in Galois theories
  • F. Beukers -- Notes on \(A\)-hypergeometric functions
  • V. Bosser and F. Pellarin -- Drinfeld \(A\)-quasi-modular forms
  • G. Casale -- An introduction to Malgrange pseudogroup
  • B. Chiarellotto< -- An invitation to p-adic differential equations (Edited with the aid of G. Gerotto and F. Sullivan)
  • L. Di Vizio and J. Sauloy -- Outils pour la classification locale des equations aux \(q\)-differences linéaires complexes
  • C. Hardouin -- Unipotent radicals of Tannakian Galois groups in positive characteristic
  • C. Krattenthaler and T. Rivoal -- Multivariate \(p\)-adic formal congruences and integrality of Taylor coefficients of mirror maps
  • A. Pulita -- A basic introduction to deformation and confluence of ultrametric differential and \(q\)-difference equations
  • J. Roques -- On the Galois groups of families of regular singular difference systems
  • V. P. Spiridonov -- Elliptic hypergeometric terms
  • B. Chiarellotto<, G. Gerotto, and F. J. Sullivan< -- Dwork's 1994 Padova lectures on exponential modules
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