p-adic Differential Equations (Google eBook)

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Cambridge University Press, Jun 10, 2010 - Mathematics
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Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
  

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Contents

0 Introductory remarks
1
Part I Tools of padic Analysis
11
Part II Differential Algebra
75
Part III padic Differential Equations on Discs and Annuli
133
Part IV Difference Algebra and Frobenius Modules
241
Part V Frobenius Structures
289
Part VI Areas of Application
345
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About the author (2010)

Kiran S. Kedlaya is Associate Professor of Mathematics at Massachusetts Institute of Technology, Cambridge, USA.

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