Introduction To Algebraic And Abelian Functions

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Introduction To Algebraic And Abelian Functions

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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Algebraic And Abelian Functions written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.

Introduction To Algebraic And Abelian Functions 2nd Ed

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Author : Serge Lang
language : en
Publisher:
Release Date : 1982

Introduction To Algebraic And Abelian Functions 2nd Ed written by Serge Lang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.

Introduction To The Classical Theory Of Abelian Functions

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Author : Alekseĭ Ivanovich Markushevich
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Introduction To The Classical Theory Of Abelian Functions written by Alekseĭ Ivanovich Markushevich 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 1992 with Mathematics categories.

The theory of Abelian functions, which was at the center of nineteenth-century mathematics, is again attracting attention. However, today it is frequently seen not just as a chapter of the general theory of functions but as an area of application of the ideas and methods of commutative algebra. This book presents an exposition of the fundamentals of the theory of Abelian functions based on the methods of the classical theory of functions. This theory includes the theory of elliptic functions as a special case. Among the topics covered are theta functions, Jacobians, and Picard varieties. The author has aimed the book primarily at intermediate and advanced graduate students, but it would also be accessible to the beginning graduate student or advanced undergraduate who has a solid background in functions of one complex variable. This book will prove especially useful to those who are not familiar with the analytic roots of the subject. In addition, the detailed historical introduction cultivates a deep understanding of the subject. Thorough and self-contained, the book will provide readers with an excellent complement to the usual algebraic approach.

Introduction To Abelian Varieties

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Author : V. Kumar Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Introduction To Abelian Varieties written by V. Kumar Murty 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 1986 with Abelian groups categories.

This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.

Complex Abelian Varieties

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Author : Herbert Lange
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Complex Abelian Varieties written by Herbert Lange and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions.

Complex Analysis 2

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Author : Eberhard Freitag
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-10

Complex Analysis 2 written by Eberhard Freitag and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-10 with Mathematics categories.

The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.

Introduction To Abelian Varieties

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Author : Vijaya Kumar Murty
language : en
Publisher:
Release Date : 1993

Introduction To Abelian Varieties written by Vijaya Kumar Murty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Abelian varieties categories.

The book represents an introduction to the theory of abelian varieties with a view to arithmetic. The aim is to introduce some of the basics of the theory as well as some recent arithmetic applications to graduate students and researchers in other fields. The first part contains proofs of the Abel-Jacobi theorem, Riemann's relations and the Lefschetz theorem on projective embeddings over the complex numbers in the spirit of S. Lang's book Introduction to algebraic and abelian functions. Then the Jacobians of Fermat curves as well as some modular curves are discussed. Finally, as an application.

Abelian Varieties Theta Functions And The Fourier Transform

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Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21

Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.

Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.

Algebraic Equations

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Author : Edgar Dehn
language : en
Publisher: Courier Corporation
Release Date : 2012-09-05

Algebraic Equations written by Edgar Dehn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-05 with Mathematics categories.

Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.

Algebraic Function Fields And Codes

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Author : Henning Stichtenoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-20

Algebraic Function Fields And Codes written by Henning Stichtenoth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-20 with Mathematics categories.

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.