An Introduction to G-Functions

Dwork, Bernard, Giovanni Gerotto, and Francis J. Sullivan

ISBN 10: 0691036756 / ISBN 13: 9780691036755

Published by Princeton University Press, Princeton NJ, 1994

About this Item

Hardcover. An ex-library copy in original orange cloth. The usual ex-libris markings. The binding is sound, the text is clean/unmarked, and there is little cover wear. No dust jacket.

Seller Inventory # 064718

Bibliographic Details

• Title: An Introduction to G-Functions
• Publisher: Princeton University Press, Princeton NJ
• Publication Date: 1994
• Language: English
• ISBN 10: 0691036756
• ISBN 13: 9780691036755
• Binding: Hardcover
• Edition: First Edition.
• Condition: Good
• Dust Jacket Condition: No Dust Jacket
• Book Type: Book

About this title

Synopsis

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, André, 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 André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.

About the Author

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.