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Book Review

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Book Information:

Author: Andy R. Magid
Title: Lectures on differential Galois theory
Additional book information: University Lecture Series, vol. 7, Amer. Math. Soc., Providence, RI, 1994, xiii+105 pp., ISBN 0-8218-7004-1, $35.00

References [Enhancements On Off] (What's this?)

  • 1. Yves André, Quatre descriptions des groupes de Galois différentiels, Séminaire d’algèbre Paul Dubreil et Marie-Paule Malliavin (Paris, 1986) Lecture Notes in Math., vol. 1296, Springer, Berlin, 1987, pp. 28–41 (French). MR 932051, https://doi.org/10.1007/BFb0078522
  • 2. B. L. J. Braaksma and M. van der Put, Analytic and algebraic aspects of complex analytic differential equations, preprint, Groningen, 1994.
  • 3. Frits Beukers, W. Dale Brownawell, and Gert Heckman, Siegel normality, Ann. of Math. (2) 127 (1988), no. 2, 279–308. MR 932298, https://doi.org/10.2307/2007054
  • 4. Lawrence Breen, Tannakian categories, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 337–376. MR 1265536
  • 5. P. Deligne, Catégories tannakiennes, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 111–195 (French). MR 1106898
  • 6. Abdelmajid Fahim, Extensions galoisiennes d’algèbres différentielles, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 1, 1–4 (French, with English summary). MR 1149627, https://doi.org/10.2140/pjm.1997.180.7
  • 7. E. Galois, Mémoire sur les conditions de résolubilité des équations par radicaux (R. Bourgne and J.-P. Azra, eds.), Gauthiers-Villars, 1962. [The quotation reads as follows: ``que toute fonction des racines, déterminable rationnellement, soit invariable par ces substitutions.'']
  • 8. Irving Kaplansky, An introduction to differential algebra, Actualités Sci. Ind., No. 1251 = Publ. Inst. Math. Univ. Nancago, No. 5, Hermann, Paris, 1957. MR 0093654
  • 9. N. Katz, A conjecture in the arithmetic theory of differential equations, Bull. Soc. Math. France 110 (1982), 203--239.
  • 10. Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536
  • 11. E. Kolchin, Existence theorems connected with the Picard-Vessiot theory of homogeneous LODE, Bull. Amer. Math. Soc. 54 (1948), 927--932. MR 10:349a
  • 12. E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York-London, 1973. Pure and Applied Mathematics, Vol. 54. MR 0568864
  • 13. J. Kovacic, On the inverse problem in the Galois theory of differential fields. II., Ann. of Math. (2) 93 (1971), 269–284. MR 0285514, https://doi.org/10.2307/1970775
  • 14. Michio Kuga, Galois’ dream: group theory and differential equations, Birkhäuser Boston, Inc., Boston, MA, 1993. Translated from the 1968 Japanese original by Susan Addington and Motohico Mulase. MR 1199112
  • 15. C. Mitschi and M. Singer, Connected linear groups as differential Galois groups, to appear in J. Algebra.
  • 16. Jean-Pierre Ramis, Phénomène de Stokes et filtration Gevrey sur le groupe de Picard-Vessiot, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 5, 165–167 (French, with English summary). MR 801953
  • 17. Jean-Pierre Serre, Gèbres, Enseign. Math. (2) 39 (1993), no. 1-2, 33–85 (French). MR 1225256
  • 18. Michael F. Singer and Felix Ulmer, Galois groups of second and third order linear differential equations, J. Symbolic Comput. 16 (1993), no. 1, 9–36. MR 1237348, https://doi.org/10.1006/jsco.1993.1032

Review Information:

Reviewer: D. Bertrand
Affiliation: Institut de Mathématiques, Université de Paris VI
Email: bertrand@mathp6.jussieu.fr
Journal: Bull. Amer. Math. Soc. 33 (1996), 289-294
DOI: https://doi.org/10.1090/S0273-0979-96-00652-0
Review copyright: © Copyright 1996 American Mathematical Society