# Introduction to the classical theory of Abelian functions

- 175 Pages
- 1992
- 1.98 MB
- 7691 Downloads
- English

American Mathematical Society , Providence, R.I

Functions, Ab

Statement | A.I. Markushevich ; [translated from the Russian by G. Bluher ; translation edited by Ralph P. Boas]. |

Series | Translations of mathematical monographs ;, v. 96 |

Contributions | Boas, Ralph Philip. |

Classifications | |
---|---|

LC Classifications | QA345 .M4513 1992 |

The Physical Object | |

Pagination | viii, 175 p. : |

ID Numbers | |

Open Library | OL1556403M |

ISBN 10 | 082184542X |

LC Control Number | 91036838 |

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 by: By A.

Markushevich, pp., US$, ISBN 0 X (American Mathematical Society, ).Author: W. Hayman. Presents an exposition of the fundamentals of the theory of Abelian functions based on the methods of the classical theory of functions. This book covers such topics as theta functions, Jacobians, and Picard varieties.

Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory.

### Description Introduction to the classical theory of Abelian functions EPUB

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.

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.

Show synopsis 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.4/5(1). A very classical introduction is Swinnerton-Dyer's Analytic theory of abelian varieties (London Mathematical Society Lecture Note Series 14).

Another good place to start is M. Schlichenmaier, An introduction to Riemann surfaces, algebraic curves and moduli spaces, Theoretical and Mathematical Physics, Springer-Verlag (2nd ed.). The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group.

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(ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a. Introduction to Classical Field Theory.

Charles G. Torre. Department of Physics, Utah State University, @ Follow this and additional works at: Part of the Applied Mathematics Commons, Cosmology, Relativity, and Gravity Commons, : Charles G Torre.

An abelian function is a meromorphic function on an abelian variety, which may be regarded therefore as a periodic function of n complex variables, having 2n independent periods; equivalently, it is a function in the function field of an abelian variety.

Math B. Geometric global class field theory 1. Introduction Class eld theory for global function elds Kover nite constant elds kcan be reformulated in purely algebro-geometric terms, as a theory of nite abelian coverings of smooth projective algebraic curves over nite elds (with controlled rami cation over the base curve).

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.

An Abelian function $ f (z) $ is said to be degenerate if there exists a linear transformation of the variables $ z _ {1} \dots z _ {p} $ which converts $ f(z) $ into a function of fewer variables; otherwise $ f(z) $ is said to be a non-degenerate Abelian function.

Degenerate Abelian functions are distinguished by having infinitely small. Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. 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 Translations of Mathematical Monographs: : A. Markushevich: Libros en idiomas extranjerosAuthor: A. Markushevich. Introduction to Algebraic and Abelian Functions by Serge Lang,available at Book Depository with free delivery worldwide/5(6).

The equivariant theory of Abelian functions. Another recent area of study has been the equivariant theory of Abelian functions. This is an alternative approach to the functions where the underlying curves are redefined so that both the curve and functions transform under a group action allowing for the use of representation theory.

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 : $ This chapter focuses on abelian gauge theory, whose physical realization is Quantum Electrodynamics (QED).

The chapter is organized as follows. It begins with elementary considerations about the massive vector field in perturbation theory.

It shows that coupling to matter field leads to field theories that are renormalizable in four dimensions only if the vector. Fishpond United Kingdom, Introduction to Algebraic and Abelian Functions (Graduate Texts in Mathematics) by SergeLangBuy.

Books online: Introduction to Algebraic and Abelian Functions (Graduate Texts in Mathematics), ⋆⋆ The goals of this book 18 Part I. Preliminaries 21 Chapter 1. Some category theory 23 Motivation 23 Categories and functors 25 Universal properties determine an object up to unique isomorphism 31 Limits and colimits 39 Adjoints 43 An introduction to abelian categories 46 ⋆ Spectral sequences However, in proceeding quickly and efficiently to the main subjects of the book, the author omits from the first two chapters some concrete examples from the classical theory which have historical and motivational value, e.g., q-expansion computations for Eisenstein series (given later in Chapter X), relations with the Weierstrass wp-function.

The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles. The purpose of these notes is to present some basic facts of this theory to make this book more self contained. In particular we will deal with classical descriptions of Riemann surfaces, Abelian differentials, periods on Riemann surfaces, meromorphic functions.

This chapter constructs a field theory invariant under local, that is, space-dependent, transformations of a general compact Lie group G.

Inspired by the abelian example of Chap it introduces the geometric concept of parallel transport — a concept discussed more extensively in Chapter 22 in the example of Riemannian manifolds. All the required. ABELIAN VARIETIES, THETA FUNCTIONS AND One of the main goals of this book is to present an introduction to the algebraic theory of abelian varieties in which Rather, its purpose is to enhance this classical theory with more recent ideas and to consider it in a slightly different perspective.

Number theory and algebra play an increasingly signiﬁcant role in computing and communications, as evidenced by the striking applications of these subjects to such ﬁelds as cryptography and coding theory. My goal in writing this book was to provide an introduction to number theory and algebra, with an emphasis.

Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U (2) theory relevant for electroweak interactions/5(3). Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on finite graphs.

Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. The resulting theory of divisors on graphs runs in close parallel to the geometric theory of divisors on Riemann surfaces, and Part 1 culminates in a full exposition of the graph.

Number Theory Books, P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.)N. Koblitz, Graduate T Springer Algorithmic Number Theory, Vol. 1, E. Bach and J.

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Shallit, MIT Press, August ; Automorphic Forms and Representations, D. Bump, CUP ; Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical.

I W.-K. Tung, Group Theory in Physics (World Scienti c, ). general introduction; main focus on continuous groups I L. Falicov, Group Theory and Its Physical Applications (University of Chicago Press, Chicago, ). small paperback; compact introduction I E. Wigner, Group Theory (Academic, ).

classical textbook by the master. The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles.

The purpose of these notes is to present some basic facts of this.Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject.

The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a .The aim is, firstly, to bring out clearly the relations between classical analysis and group theory, and secondly, to study basic properties of functions on abelian and non-abelian groups.

The book gives a systematic introduction to these topics and .