An Introduction to G-Functions by Bernard Dwork
Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, Andre, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and Andre on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.-
The Girth Ramsey Theorem
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Riemann Surfaces and Related Topics
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Seminar on the Atiyah-Singer Index Theorem
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Lectures on Curves on an Algebraic Surface
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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik
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The Einstein-Klein-Gordon Coupled System
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A Hierarchy of Turing Degrees
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Elementary Differential Topology
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Some Problems of Unlikely Intersections in Arithmetic and Geometry
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The Norm Residue Theorem in Motivic Cohomology
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The Structure of Groups with a Quasiconvex Hierarchy
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Curvature and Betti Numbers
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Period Spaces for p-divisible Groups
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Exponential Sums and Differential Equations
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Functional Operators, Volume 2
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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
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The Decomposition of Global Conformal Invariants
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Weyl Group Multiple Dirichlet Series
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Green's Function Estimates for Lattice Schroedinger Operators and Applications. (AM-158)
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Automata Studies
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Arithmetic and Geometry
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Stationary Processes and Prediction Theory
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Seminar on Singularities of Solutions of Linear Partial Differential Equations
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Contributions to Fourier Analysis
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Unipotent Ideals and Harish-Chandra Bimodules
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Hoelder Continuous Euler Flows in Three Dimensions with Compact Support in Time
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Non-Archimedean Tame Topology and Stably Dominated Types
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The p-adic Simpson Correspondence
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The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
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Contributions to the Theory of Games, Volume IV
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Seminar on Micro-Local Analysis
"[This book] is well suited for a graduate course, its value as a textbook being enhanced by working out several concrete examples and counterexamples of the phenomena studied in the book"--Mathematical Reviews
Bernard Dwork is Professor of Mathematics at Princeton University. Giovanni Gerotto and Francis J. Sullivan are Associate Professors of Mathematics at the University of Padova.
| SKU | Unavailable |
| ISBN 13 | 9780691036816 |
| ISBN 10 | 0691036810 |
| Title | An Introduction to G-Functions |
| Author | Bernard Dwork |
| Series | Annals Of Mathematics Studies |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Princeton University Press |
| Year published | 1994-05-22 |
| Number of pages | 352 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |