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Author: Bernard Dwork
Publisher: Princeton University Press
ISBN: 0691036810
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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.
Author: Bernard Dwork
Publisher: Princeton University Press
ISBN: 0691036810
Category : Mathematics
Languages : en
Pages : 348
Get Book
Book Description
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.
Author: Bernard Dwork
Publisher: Princeton University Press
ISBN: 1400882540
Category : Mathematics
Languages : en
Pages : 349
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Book Description
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.
Author: Bernard Dwork
Publisher: Princeton University Press
ISBN: 1400882540
Category : Mathematics
Languages : en
Pages : 349
Get Book
Book Description
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.
Author: Parimal Mukhopadhyay
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842651636
Category : Business & Economics
Languages : en
Pages : 252
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Book Description
The theory of estimating functions plays a major role in analysis of data pertaining to Biostatistics, Econometrics, Time Series Analysis, Reliability studies and other varied fields. This book discusses at length the application of the theory in interpretation of results in Survey Sampling.
Author: Jun-ichi Igusa
Publisher: American Mathematical Soc.
ISBN: 0821829076
Category : Mathematics
Languages : en
Pages : 246
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Book Description
This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Author: Carlo Viola
Publisher: Springer
ISBN: 3319413457
Category : Mathematics
Languages : en
Pages : 168
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Book Description
The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special functions: the Euler gamma function, the Gauss hypergeometric function, and the Kummer confluent hypergeometric function. Such special functions are indispensable tools in "higher calculus" and are frequently encountered in almost all branches of pure and applied mathematics. The only knowledge assumed on the part of the reader is an understanding of basic concepts to the level of an elementary course covering the residue theorem, Cauchy's integral formula, the Taylor and Laurent series expansions, poles and essential singularities, branch points, etc. The book addresses the needs of advanced undergraduate and graduate students in mathematics or physics.
Author: Yves André
Publisher: Vieweg+teubner Verlag
ISBN:
Category : Mathematics
Languages : de
Pages : 248
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Book Description
This is an introduction to some geometrie aspects of G-function theory. Most of the results presented here appear in print for the flrst time; hence this text is something intermediate between a standard monograph and a research artic1e; it is not a complete survey of the topic. Except for geometrie chapters (I.3.3, II, IX, X), I have tried to keep it reasonably self contained; for instance, the second part may be used as an introduction to p-adic analysis, starting from a few basic facts wh ich are recalled in IV.l.l. I have inc1uded about forty exercises, most of them giving some complements to the main text. Acknowledgements This book was written during a stay at the Max-Planck-Institut in Bonn. I should like here to express my special gratitude to this institute and its director, F. Hirzebruch, for their generous hospitality. G. Wüstholz has suggested the whole project and made its realization possible, and this book would not exist without his help; I thank him heartily. I also thank D. Bertrand, E. Bombieri, K. Diederich, and S. Lang for their encouragements, and D. Bertrand, G. Christo I and H Esnault for stimulating conversations and their help in removing some inaccuracies after a careful reading of parts of the text (any remaining error is however my sole responsibility).
Author: W.T. Ingram
Publisher: Springer Science & Business Media
ISBN: 146144487X
Category : Mathematics
Languages : en
Pages : 93
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Book Description
Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful.
Author: Henry Frederick Baker
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 370
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Book Description
Author: Sir M. J. Lighthill
Publisher: Cambridge University Press
ISBN: 9780521091282
Category : Mathematics
Languages : en
Pages : 112
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Book Description
"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress
