A01=Bernard Dwork
A01=Francis J. Sullivan
A01=Giovanni Gerotto
Algebraic closure
Algebraic Method
Algebraic number field
Algebraic variety
Algebraically closed field
Analytic continuation
Analytic function
Argument principle
Author_Bernard Dwork
Author_Francis J. Sullivan
Author_Giovanni Gerotto
Automorphism
Binomial series
Category=PBH
Category=PBKJ
Cauchy sequence
Cauchy's theorem (geometry)
Coefficient
Cohomology
Commutative ring
Complete intersection
Density theorem
Differential equation
Dimension (vector space)
Discrete valuation
Eigenvalues and eigenvectors
Elliptic curve
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Existential quantification
Exponential function
Exterior algebra
Field of fractions
Finite field
Formal power series
Fuchs' theorem
G-module
Galois extension
Galois group
General linear group
Generic point
Geometry
Hypergeometric function
Identity matrix
Laurent series
Limit of a sequence
Linear differential equation
Mathematical induction
Meromorphic function
Monodromy
Monotonic function
Multiplicative group
Natural number
Newton polygon
Number theory
P-adic number
Parameter
Polynomial
Projective line
Quadratic residue
Radius of convergence
Rational number
Residue field
Riemann hypothesis
Ring of integers
Root of unity
Separable polynomial
Siegel's lemma
Special case
Subring
Summation
Theorem
Topology of uniform convergence
Triangle inequality
Valuation ring
Weil conjecture
Product details
- ISBN 9780691036816
- Weight: 510g
- Dimensions: 197 x 254mm
- Publication Date: 22 May 1994
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
