Introduction to Algebraic and Abelian Functions

Introduction to Algebraic and Abelian Functions PDF

Author: Serge Lang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 178

ISBN-13: 1461257409

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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 the Classical Theory of Abelian Functions

Introduction to the Classical Theory of Abelian Functions PDF

Author: Alekse_ Ivanovich Markushevich

Publisher: American Mathematical Soc.

Published: 2006-07-26

Total Pages: 188

ISBN-13: 9780821898369

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Historical introduction. The Jacobian inversion problem Periodic functions of several complex variables Riemann matrices. Jacobian (intermediate) functions Construction of Jacobian functions of a given type. Theta functions and Abelian functions. Abelian and Picard manifolds Appendix A. Skew-symmetric determinants Appendix B. Divisors of analytic functions Appendix C. A summary of the most important formulas

Algebraic Functions

Algebraic Functions PDF

Author: Kenkichi Iwasawa

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 314

ISBN-13: 0821819690

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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.

Introduction to Abelian Varieties

Introduction to Abelian Varieties PDF

Author: Vijaya Kumar Murty

Publisher:

Published: 1993

Total Pages: 112

ISBN-13: 9781470438494

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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.

Algebraic Numbers and Algebraic Functions

Algebraic Numbers and Algebraic Functions PDF

Author: P.M. Cohn

Publisher: CRC Press

Published: 2018-01-18

Total Pages: 204

ISBN-13: 1351078038

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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.

Introduction to Abelian Varieties

Introduction to Abelian Varieties PDF

Author: V. Kumar Murty

Publisher: American Mathematical Soc.

Published: 1986

Total Pages: 136

ISBN-13: 9780821870051

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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.

An Introduction to Algebraic Geometry and Algebraic Groups

An Introduction to Algebraic Geometry and Algebraic Groups PDF

Author: Meinolf Geck

Publisher: Oxford University Press

Published: 2013-03-14

Total Pages: 321

ISBN-13: 019967616X

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An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.

Abelian Functions

Abelian Functions PDF

Author: Henry Frederick Baker

Publisher: Cambridge University Press

Published: 1995-12-14

Total Pages: 724

ISBN-13: 9780521498777

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Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century it has been enriched by the methods and ideas of topology, commutative algebra and Grothendieck's schemes seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This book contains more than its modest title suggests. Written in 1897, its scope was as broad as it could possibly be, namely to cover the whole of algebraic geometry, and associated theories. The subject is discussed by Baker in terms of transcendental functions, and in particular theta functions. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.

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