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:
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.
Download or read book Theory of Algebraic Functions of One Variable written by Richard Dedekind and published by American Mathematical Society(RI). This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1882 Theorie der algebraischen Functionen einer Veränderlichen by Dedekind (1831-1916) and Weber (1842-1913) changed the direction of algebraic geometry and established its foundations by introducing methods from algebraic number theory. They used rings and ideals to give rigorous proofs of results that had previously been obtained in non-rigorous fashion, with the help of analysis and topology. Stillwell (mathematics, U. of San Francisco) believes that the paper still has gems for modern mathematicians that the standard commentaries do not mention. He presents the first English translation of it and provides commentary to the language and thinking of mathematics during the 19th century. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
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.
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.
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.
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:
Download or read book Algebraic Function Fields and Codes written by Henning Stichtenoth and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Download or read book Some Results in the Theory of Algebraic Functions of One Variable written by Isabel (Fields) Muhly and published by . This book was released on 1942 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A New Method in the Theory of Algebraic Functions of One Variable written by Mary Jean Fisher and published by . This book was released on 1933 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Number Theory written by Helmut Koch and published by American Mathematical Soc.. This book was released on 2000 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Download or read book On the Foundations of the Theory of Algebraic Functions of One Variable written by John Charles Fields and published by . This book was released on 1913 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Algebraic Numbers and Algebraic Functions written by Emil Artin and published by American Mathematical Soc.. This book was released on 2005 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
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.
Download or read book On the Foundations of the Theory of Algebraic Functions of One Variable nby J C Fields Ph D Associate Professor of Mathematics in the University of Toronto written by John Charles Fields and published by . This book was released on 1913 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
