1.

Record Nr.

UNINA9910154744303321

Autore

Dwork Bernard

Titolo

An Introduction to G-Functions. (AM-133), Volume 133 / / Bernard Dwork, Francis J. Sullivan, Giovanni Gerotto

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©1994

ISBN

1-4008-8254-0

Descrizione fisica

1 online resource (349 pages) : illustrations

Collana

Annals of Mathematics Studies ; ; 316

Disciplina

515/.55

Soggetti

H-functions

p-adic analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Frontmatter -- CONTENTS -- PREFACE / Dwork, B. -- INTRODUCTION -- LIST OF SYMBOLS -- CHAPTER I. VALUED FIELDS -- CHAPTER II. ZETA FUNCTIONS -- CHAPTER III. DIFFERENTIAL EQUATIONS -- CHAPTER IV. EFFECTIVE BOUNDS. ORDINARY DISKS -- CHAPTER V. EFFECTIVE BOUNDS. SINGULAR DISKS -- CHAPTER VI. TRANSFER THEOREMS INTO DISKS WITH ONE SINGULARITY -- CHAPTER VII. DIFFERENTIAL EQUATIONS OF ARITHMETIC TYPE -- CHAPTER VIII. G-SERIES. THE THEOREM OF CHUDNOVSKY -- APPENDIX I. CONVERGENCE POLYGON FOR DIFFERENTIAL EQUATIONS -- APPENDIX II. ARCHIMEDEAN ESTIMATES -- APPENDIX III. CAUCHY'S THEOREM -- BIBLIOGRAPHY -- INDEX

Sommario/riassunto

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.

2.

Record Nr.

UNISA990003691650203316

Autore

DIOSCORIDES, Pedanius

Titolo

[Pedanij Dioscoridis Anazarbei De medicinali materia, libri sex, Ioanne Ruellio Suessionensi interprete. Cuilibet capiti additae Annotationes, erudiditae & compendiariae, è selectiori Medicorum promptuario]

Pubbl/distr/stampa

Lugduni, : apud Balthazarem Arnolletum, 1550

Descrizione fisica

[32], 790, [2] p. : ill. ; 8°

Collocazione

F.V. II B 51

Lingua di pubblicazione

Latino

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Dati del frontespizio ricavati da SBN, che segnala anche la presenza di una marca raffigurante Cavallo marino che regge una spada dai cui bracci pendono piatti da una bilancia