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Book Introduction to the Theory of Algebraic Functions of One Variable

Download or read book Introduction to the Theory of Algebraic Functions of One Variable written by Claude Chevalley and published by American Mathematical Soc.. This book was released on 1951-12-31 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.

Book Theory of Algebraic Functions of One Variable

Download or read book Theory of Algebraic Functions of One Variable written by Richard Dedekind and published by American Mathematical Soc.. This book was released on 2012-07-23 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator's Introduction that includes historical background, and also by extensive commentary embedded in the translation itself. The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians. Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann's arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation. The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind's theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.

Book Algebraic Numbers and Algebraic Functions

Download or read book Algebraic Numbers and Algebraic Functions written by P.M. Cohn and published by CRC Press. This book was released on 2018-01-18 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.

Book Introduction to the Theory of Algebraic Numbers and Functions

Download or read book Introduction to the Theory of Algebraic Numbers and Functions written by Martin Eichler and published by . This book was released on 1966 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves to introduce the general notions, the concepts, and the methods which underlie the theories of algebraic numbers and algebraic functions, primarily in one variable. It also introduces the theory of elliptic modular functions, which has deep applications in analytic number theory.

Book Topics in the Theory of Algebraic Function Fields

Download or read book Topics in the Theory of Algebraic Function Fields written by Gabriel Daniel Villa Salvador and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

Book Introduction to Classical Mathematics I

Download or read book Introduction to Classical Mathematics I written by Helmut Koch and published by Springer Science & Business Media. This book was released on 1991-05-31 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 6Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the human mce. It has put common sense back je n'y serais point alle.' Jules Verne where it belongs, on the topmost shelf nCllt to the dusty canister labelled 'discarded non­ sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com­ puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Book Introductory Notes on Valuation Rings and Function Fields in One Variable

Download or read book Introductory Notes on Valuation Rings and Function Fields in One Variable written by Renata Scognamillo and published by Springer. This book was released on 2014-07-01 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert’s Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons.

Book Theory of Algebraic Functions of One Variable

Download or read book Theory of Algebraic Functions of One Variable written by Richard Dedekind and published by . This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Theory of the Algebraic Functions of a Complex Variable

Download or read book Theory of the Algebraic Functions of a Complex Variable written by John Charles Fields and published by Berlin : Mayer & Müller. This book was released on 1906 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Theory of the Algebraic Functions of a Complex Variable

Download or read book Theory of the Algebraic Functions of a Complex Variable written by John Charles Fields and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced mathematical text is a detailed exploration of complex variable theory. It covers topics such as integrals, series expansions, and conformal mapping. While it is a challenging read, it is also a seminal work in the field of mathematics and is still widely studied today. Mathematicians and math students will find this book to be an invaluable resource. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Book Theory of the Algebraic Functions of a Complex Variable

Download or read book Theory of the Algebraic Functions of a Complex Variable written by John Charles Fields and published by Forgotten Books. This book was released on 2015-06-25 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Theory of the Algebraic Functions of a Complex Variable The theory of the algebraic functions developed in the following pages is algebraic in its methods and perfectly general. It holds for any algebraic equation reducible or irreducible, however complicated its singularities may be and whatever its character at infinity. The development of the theory may be said to culminate in the complementary theorem, in Chapter XII, from which theorem a number of well-known theorems in the theory of the algebraic functions immediately follow as corollaries. The principles here presented have been in the possession of the writer for some eight years past and had in fact, in a somewhat different form, already been written up with a view to publication in the summer of 1898. Other matters however intervened and the work was laid aside for a long period. Since then further interruptions have occurred, - the theory however has been twice rewritten in the interval and has probably lost nothing by the delay in publication. The writer has not felt it to be necessary to go into the theory of the Abelian integrals, his object having been attained on presenting the purely algebraic side of his subject. The principle embodied in the statement of the limitation on the orders of coincidence which a reduced form can have simultaneously with then branches of the fundamental algebraic equation, is evidently of wider scope than the theory of the algebraic functions. Also the method of the deformation of a product, or its equivalent, should find its application elsewhere, for example in the theory of the algebraic numbers and in the theory of the algebraic functions of several variables. In the latter connection the writer might say that he possesses a simple representation of the branches of an algebraic function of any number of variables in the neighborhood of a singular manifold and hopes to be able to utilize this representation in combination with the methods employed in the present volume. In conclusion the writer desires to express his thanks to Professor Mittag-Leffler and Professor Phragmén for the interest they have taken in his work. Acknowledgement is also due to the publishers, Messrs Mayer and Muller, for the obliging readiness with which they have always met the wishes of the author. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Oeuvres Scientifiques   Collected Papers

Download or read book Oeuvres Scientifiques Collected Papers written by André Weil and published by Springer Science & Business Media. This book was released on 2009-01-30 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century. Part of a three-volume set, this work collects his papers in chronological order and includes lengthy commentaries on many of the articles written by Weil himself.

Book Algebraic Functions

    Book Details:
  • Author : Kenkichi Iwasawa
  • Publisher : American Mathematical Soc.
  • Release : 1993
  • ISBN : 0821819690
  • Pages : 314 pages

Download or read book Algebraic Functions written by Kenkichi Iwasawa and published by American Mathematical Soc.. This book was released on 1993 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a translation of Iwasawa's 1973 book, Theory of Algebraic Functions originally published in Japanese. Because the book treats mainly the classical part of the theory of algebraic functions, emphasizing analytic methods, it provides an excellent introduction to the subject from the classical viewpoint. Directed at graduate students, the book requires some basic knowledge of algebra, topology, and functions of a complex variable.

Book Lectures on the Theory of Algebraic Functions of One Variable

Download or read book Lectures on the Theory of Algebraic Functions of One Variable written by Max Deuring and published by Springer. This book was released on 2006-11-15 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Algebraic Functions and Projective Curves

Download or read book Algebraic Functions and Projective Curves written by David Goldschmidt and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves.

Book Function Theory of One Complex Variable

Download or read book Function Theory of One Complex Variable written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

Book Algebraic Numbers and Algebraic Functions

Download or read book Algebraic Numbers and Algebraic Functions written by P.M. Cohn and published by CRC Press. This book was released on 2018-01-18 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.