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A satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters, has developed in recent years. This comprehensive account of the subject provides a unified foundation for the theory to which I.G. Macdonald has been a principal contributor. The first four chapters lead up to Chapter 5 which contains all the main results.

Roswitha Hecke's photo book Liebes Leben (Love Life) about the Zurich artist-muse and prostitute, Irene, also called "Lady Shiva," was published for the first time in 1978. It became both a cult book and an international success. Reprinted many times and translated into several languages, it is finally available again. The new, revised volume put out by Edition Patrick Frey presents photos that have never before been published. It is through the director Werner Schroeter that Roswitha Hecke met Irene. Irene, a secret star of Zurich's Boheme at that time, worked as a prostitute until her tragic accidental death. For three weeks Hecke photographed her daily routine in Zurich and accompanied her to Rome where Irene always celebrated her birthday. The result was a subtle and strong portrait of a woman, both beautiful and confident, with an unrivaled eroticism and proud elegance. The photos, a mix of choreographed and documentary work, capture an unusual immediacy and presence. Irene wanted to be pretty, to be a woman, to be free. She was direct and moody, like a child. She loved a flirt more than marriage. Tension more than harmony. Longing more than satisfaction. And distance more than contact. She lived her life according to this, come what may.

When the Hamburg photographer Roswitha Hecke moved to Paris, she rented a room in Pigalle with an eye to photographing the neighborhood's prostitutes. She had presumed her subjects would be women, but she found herself living on a block known for its transsexuals. She stayed for months, settling in, making friends, getting closer to her unexpected subjects. Their comfort in her presence is clear in these uncannily intimate portraits. Back at home she returned to a career in film photography, where her collaborators have included Rainer Werner Fassbinder and Werner Schroeter, and in artist portraits, where her subjects have included William S. Burroughs, Paul Bowles and Ian McEwan. Hecke brings a matter-of-fact clarity, and a special kind of intimacy, to both stardom and the underworld.

German language. 8.46x4.92x0.87 inches. In Stock.

The numerous explicit formulae of the classical theory of quadratic forms revealed remarkable multiplicative properties of the numbers of integral representations of integers by positive definite integral quadratic forms. These properties were explained by the original theory of Hecke operators. As regards the integral representations of quadratic forms in more than one variable by quadratic forms, no multiplicative properties were known at that time, and so there was nothing to explain. However, the idea of Hecke operators was so natural and attractive that soon attempts were made to cultivate it in the neighbouring field of modular forms of several variables. The approach has proved to be fruitful; in particular, a number of multiplicative properties of integral representations of quadratic forms by quadratic forms were eventually discovered. By now the theory has reached a certain maturity, and the time has come to give an up-to-date report in a concise form, in order to provide a solid ground for further development. The purpose of this book is to present in the form of a self-contained text-book the contemporary state of the theory of Hecke operators on the spaces of hoi om orphic modular forms of integral weight (the Siegel modular forms) for congruence subgroups of integral symplectic groups. The book can also be used for an initial study of modular forms of one or several variables and theta-series of positive definite integral quadratic forms.

Roswitha Hecke's photo book Liebes Leben (Love Life) about the Zurich artist-muse and prostitute, Irene, also called "Lady Shiva," was published for the first time in 1978. It became both a cult book and an international success. Reprinted many times and translated into several languages, it is finally available again. The new, revised volume put out by Edition Patrick Frey presents photos that have never before been published. It is through the director Werner Schroeter that Roswitha Hecke met Irene. Irene, a secret star of Zurich's Boheme at that time, worked as a prostitute until her tragic accidental death. For three weeks Hecke photographed her daily routine in Zurich and accompanied her to Rome where Irene always celebrated her birthday. The result was a subtle and strong portrait of a woman, both beautiful and confident, with an unrivaled eroticism and proud elegance. The photos, a mix of choreographed and documentary work, capture an unusual immediacy and presence. Irene wanted to be pretty, to be a woman, to be free. She was direct and moody, like a child. She loved a flirt more than marriage. Tension more than harmony. Longing more than satisfaction. And distance more than contact. She lived her life according to this, come what may.

A satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters, has developed in recent years. This comprehensive account of the subject provides a unified foundation for the theory to which I.G. Macdonald has been a principal contributor. The first four chapters lead up to Chapter 5 which contains all the main results.

This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Modern number theory, according to Hecke, dates from Gauss's quadratic reciprocity law. The various extensions of this law and the generalizations of the domains of study for number theory have led to a rich network of ideas, which has had effects throughout mathematics, in particular in algebra. This volume of the Encyclopaedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Koch has written for the non-specialist. He assumes that the reader has a general understanding of modern algebra and elementary number theory. Mostly only the general properties of algebraic number fields and related structures are included. Special results appear only as examples which illustrate general features of the theory. A part of algebraic number theory serves as a basic science for other parts of mathematics, such as arithmetic algebraic geometry and the theory of modular forms. For this reason, the chapters on basic number theory, class field theory and Galois cohomology contain more detail than the others. This book is suitable for graduate students and research mathematicians who wish to become acquainted with the main ideas and methods of algebraic number theory.

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Modern number theory, according to Hecke, dates from Gauss's quadratic reciprocity law. The various extensions of this law and the generalizations of the domains of study for number theory have led to a rich network of ideas, which has had effects throughout mathematics, in particular in algebra. This volume of the Encyclopaedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Koch has written for the non-specialist. He assumes that the reader has a general understanding of modern algebra and elementary number theory. Mostly only the general properties of algebraic number fields and related structures are included. Special results appear only as examples which illustrate general features of the theory. A part of algebraic number theory serves as a basic science for other parts of mathematics, such as arithmetic algebraic geometry and the theory of modular forms. For this reason, the chapters on basic number theory, class field theory and Galois cohomology contain more detail than the others. This book is suitable for graduate students and research mathematicians who wish to become acquainted with the main ideas and methods of algebraic number theory.

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.