Progress towards an understanding of the dynamics and interactions of galaxies has been spurred on more than ever by a wealth of new observations and numerical experiments. The Heidelberg Conference 1989, the papers of which are collected in this volume, was extremely successful in presenting a synoptic view of the field in all its aspects: galaxy interactions in the early universe and in recent times, interactions of our galaxy and its neighbours, dynamical problems of elliptical and disk galaxies, groups and clusters, starburst and nuclear activity triggered by interactions, merger scenarios, and numerical experiments. Researchers and graduate students, specialists or not, will find here a complete overview of a rapidly growing field of astronomy.

Elementary Dirichlet Series and Modular Forms

Science & Math

Shimura, Goro

Astronomy & Space Science

Springer

This is a textbook for Riemannian Geometry and Geometric Analysis, introducing techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensible tool in research in geometry and they are treated in a textbook for the first time. Subjects treated are: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles, the Hodge theorem for de Rham cohomology, connections and curvature, the Yang-Mills functional, geodesics and Jacobi fields, Rauch comparison theorem and applications, Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics, symmetric spaces and Kahler manifolds, the Palais-Smale condition and closed geodesics, harmonic maps, definition and basic properties, existence and uniqueness theorems, applications, minimal surfaces, regularity results. In an appendix Sobolev spaces and regularity theory for linear elliptic equations are discussed in detail. The book gives both invariant global notation and tensor notation and should thus prove to be of interest to physicists as well.

The Map of My Life (Universitext)

Mathematics

A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.

Elementary Dirichlet Series and Modular Forms (Springer Monographs in Mathematics)

In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.
Goro Shimura is Professor Emeritus of Mathematics at Princeton University. In 1996, he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. He is the author of Elementary Dirichlet Series and Modular Forms (Springer 2007), Arithmeticity in the Theory of Automorphic Forms (AMS 2000), and Introduction to the Arithmetic Theory of Automorphic Functions (Princeton University Press 1971).

The Map of My Life

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions.
 This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.

Abelian Varieties with Complex Multiplication and Modular Functions

Princeton University Press

The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem" Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.

Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11)

This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein series on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. 
There are various facts on algebraic groups and their localizations that are standard but were proved in some old papers or just called "well-known". In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated.

Euler Products and Eisenstein Series (Cbms Regional Conference Series in Mathematics)

Amer Mathematical Society

The main objects of study in this book are Eisenstein series and zeta functions associated with Hecke eigenforms on symplectic and unitary groups. After preliminaries--including a section, ``Notation and Terminology''--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity-law for the values of automorphic functions at CM-points is proved. Next, certain differential operators that raise the weight are investigated in higher dimension. The notion of nearly holomorphic functions is introduced, and their arithmeticity is defined. As applications of these, the arithmeticity of the critical values of zeta functions and Eisenstein series is proved. Though the arithmeticity is given as the ultimate main result, the book discusses many basic problems that arise in number-theoretical investigations of automorphic forms but that cannot be found in expository forms. Examples of this include the space of automorphic forms spanned by cusp forms and certain Eisenstein series, transformation formulas of theta series, estimate of the Fourier coefficients of modular forms, and modular forms of half-integral weight. All these are treated in higher-dimensional cases. The volume concludes with an Appendix and an Index. The book will be of interest to graduate students and researchers in the field of zeta functions and modular forms.

Arithmeticity in the Theory of Automorphic Forms (Mathematical Surveys & Monographs)

This book treats its two subjects, Dirichlet series and modular forms, in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics.

Goro Shimura is one of the world’s greatest mathematicians, and this book details his life and the strange world of the math community. It also describes life in Japan during WWII and includes Shimura’s opinions on world events and human nature.

Biographies & Memoirs

See the best price to sell, buy, or rent books by Shimura, Goro. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Shimura, Goro

See the best price to sell, buy, or rent books by Shimura, Goro. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Elementary Dirichlet Series and Modular Forms

The Map of My Life (Universitext)

Elementary Dirichlet Series and Modular Forms (Springer Monographs in Mathematics)

The Map of My Life

Abelian Varieties with Complex Multiplication and Modular Functions

Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11)

Euler Products and Eisenstein Series (Cbms Regional Conference Series in Mathematics)

Arithmeticity in the Theory of Automorphic Forms (Mathematical Surveys & Monographs)

Elementary Dirichlet Series and Modular Forms (Springer Monographs in Mathematics)

The Map of My Life