An Introduction To G Functions
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An Introduction To G Functions
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Author : Bernard Dwork
language : en
Publisher: Princeton University Press
Release Date : 1994-05-22
An Introduction To G Functions written by Bernard Dwork and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-22 with Mathematics categories.
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.
An Introduction To G Functions Am 133 Volume 133
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Author : Bernard Dwork
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
An Introduction To G Functions Am 133 Volume 133 written by Bernard Dwork and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
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.
An Introduction To Analysis
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Author : Gerald G. Bilodeau
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2009-07-28
An Introduction To Analysis written by Gerald G. Bilodeau and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-28 with Mathematics categories.
Part of the Jones and Bartlett International Series in Advanced Mathematics Completely revised and update, the second edition of An Introduction to Analysis presents a concise and sharply focused introdution to the basic concepts of analysis from the development of the real numbers through uniform convergences of a sequence of functions, and includes supplementary material on the calculus of functions of several variables and differential equations. This student-friendly text maintains a cautious and deliberate pace, and examples and figures are used extensively to assist the reader in understanding the concepts and then applying them. Students will become actively engaged in learning process with a broad and comprehensive collection of problems found at the end of each section.
Introduction To The Theory Of Entire Functions
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Author :
language : en
Publisher: Academic Press
Release Date : 1974-02-08
Introduction To The Theory Of Entire Functions written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-02-08 with Mathematics categories.
Introduction to the Theory of Entire Functions
Periodic Differential Equations
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Author : F. M. Arscott
language : en
Publisher: Elsevier
Release Date : 2014-05-16
Periodic Differential Equations written by F. M. Arscott and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.
Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation. This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and the principles of asymptotic expansions. These topics are followed by discussions of the stable and unstable solutions of Mathieu's general equation; general properties and characteristic exponent of Hill's equation; and the general nature and solutions of the spheroidal wave equation. The concluding chapters explore the polynomials, orthogonality properties, and integral relations of Lamé's equation. These chapters also describe the wave functions and solutions of the ellipsoidal wave equation. This book will prove useful to pure and applied mathematicians and functional analysis.
An Introduction To Multicomplex Spates And Functions
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Author : Price
language : en
Publisher: Routledge
Release Date : 2018-05-11
An Introduction To Multicomplex Spates And Functions written by Price and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
A rather pretty little book, written in the form of a text but more likely to be read simply for pleasure, in which the author (Professor Emeritus of Mathematics at the U. of Kansas) explores the analog of the theory of functions of a complex variable which comes into being when the complexes are re
An Introduction To The Theory Of Local Zeta Functions
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Author : Jun-ichi Igusa
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
An Introduction To The Theory Of Local Zeta Functions written by Jun-ichi Igusa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Function Classes On The Unit Disc
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Author : Miroslav Pavlović
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-08-19
Function Classes On The Unit Disc written by Miroslav Pavlović and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-19 with Mathematics categories.
This revised and extended edition of a well-established monograph in function theory contains a study on various function classes on the disc, a number of new results and new or easy proofs of old but interesting theorems (for example, the Fefferman–Stein theorem on subharmonic behavior or the theorem on conjugate functions in Bergman spaces) and a full discussion on g-functions.
An Introduction To The Approximation Of Functions
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Author : Theodore J. Rivlin
language : en
Publisher: Courier Corporation
Release Date : 1981-01-01
An Introduction To The Approximation Of Functions written by Theodore J. Rivlin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
An Introduction To The Theory Of Multiply Periodic Functions
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Author : H F Baker
language : en
Publisher: CreateSpace
Release Date : 2013-12-22
An Introduction To The Theory Of Multiply Periodic Functions written by H F Baker and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-22 with categories.
An excerpt from the PREFACE: THE present volume consists of two parts; the first of these deals with the theory of hyper-elliptic functions of two variables, the second with the reduction of the theory of general multiply-periodic functions to the theory of algebraic functions; taken together they furnish what is intended to be an elementary and self-contained introduction to many of the leading ideas of the theory of multiply-periodic functions, with the incidental aim of aiding the comprehension of the importance of this theory in analytical geometry. The first part is centred round some remarkable differential equations satisfied by the functions, which appear to be equally illuminative both of the analytical and geometrical aspects of the theory; it was in fact to explain this that the book was originally entered upon. The account has no pretensions to completeness: being anxious to explain the properties of the functions from the beginning, I have been debarred from following Humbert's brilliant monograph, which assumes from the first Poincare's theorem as to the number of zeros common to two theta functions; this theorem is reached in this volume, certainly in a generalised form, only in the last chapter of PartII.: being anxious to render the geometrical portions of the volume quite elementary, I have not been able to utilise the theory of quadratic complexes, which has proved so powerful in this connexion in the hands of Kummer and Klein; and, for both these reasons, the account given here, and that given in the remarkable book from the pen of R. W. H. T. Hudson, will, I believe, only be regarded by readers as complementary. The theory of Kummer's surface, and of the theta functions, has been much studied since the year (1847 or before) in which Gopel first obtained the biquadratic relation connecting four theta functions; and Wirtinger has shown, in his "Untersuchungen uber Thetafunctionen," which has helped me in several ways in the second part of this volume, that the theory is capable of generalisation, in many of its results, to space of "2p-1" dimensions; but even in the case of two variables there is a certain inducement, not to come to too close quarters with the details, in the fact of the existence of sixteen theta functions connected together by many relations, at least in the minds of beginners. I hope therefore that the treatment here followed, which reduces the theory, in a very practical way, to that of one theta function and three periodic functions connected by an algebraic equation, may recommend itself to others, and, in a humble way, serve the purpose of the earlier books on elliptic functions, of encouraging a wider use of the functions in other branches of mathematics. The slightest examination will show that, even for the functions of two variables, many of the problems entered upon demand further study; while, for the hyper-elliptic functions of "p" variables, for which the forms of the corresponding differential equations are known, there exist constructs, of "p" dimensions, in space of "1/2p (p+1) " dimensions, which await similar investigatio