A letter from an honourable gentleman in the court, certifying the examination of Mr. Iohn Cheisly Esquire, Secretary to the Commissioners of Scotland [[electronic resource] ] : who was taken and stayd at Newcastle, with his answer to the many interrogatories put unto him by the governour and major thereof, concerning Major-generall Massies going into Scotland, to rayse an army: and the Scots preparations to invade this kingdome. With some other advertisements concerning peace. Together with the certainty of the safe landing of Sir William Waller, Mr. Anthony Nicols, and other impeached members, at the Brill in Holland

• Record Nr.: UNISA996390784303316
• Autore: I. B
• Pubbl/distr/stampa: [London, : s.n.], Printed in the yeere, 1647
• Descrizione fisica: [2], 6 p
• Soggetti: Impeachments - England; Great Britain History Civil War, 1642-1649 Early works to 1800
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Signed at end: I.B.; Place of publication from Wing.; Annotation on Thomason copy: "Aug: 23".; Reproduction of the original in the British Library.
• Sommario/riassunto: eebo-0018

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

• Record Nr.: UNINA9910154744303321
• Autore: Dwork Bernard
• 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.