Shimura, Gorō 1930
Overview
Works:  34 works in 148 publications in 1 language and 4,782 library holdings 

Genres:  Biography History Conference proceedings 
Roles:  Author 
Classifications:  QA243, 512.74 
Publication Timeline
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Most widely held works by
Gorō Shimura
Elementary Dirichlet series and modular forms
by
Gorō Shimura(
)
10 editions published between 2007 and 2011 in English and held by 558 WorldCat member libraries worldwide
The main topics of the book are the critical values of Dirichlet Lfunctions and Hecke Lfunctions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet Lfunctions, all previous papers and books reiterate a single old result with a single old method. After a review of elementary Fourier analysis, the author presents completely new results with new methods, though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications, new formulas for the second factor of the class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge of modular forms. However, all definitions and facts are clearly stated, and precise references are given. The notion of nearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke Lfunctions of an imaginary quadratic field. Other notable features of the book are: (1) some new results on classical Eisenstein series; (2) the discussion of isomorphism classes of elliptic curves with complex multiplication in connection with their zeta function and periods; (3) a new class of holomorphic differential operators that send modular forms to those of a different weight. The book will be of interest to graduate students and researchers who are interested in special values of Lfunctions, class number formulae, arithmetic properties of modular forms (especially their values), and the arithmetic properties of Dirichlet series. It treats in detail, from an elementary viewpoint, the simplest cases of a fundamental area of ongoing research, the only prerequisite being a basic course in algebraic number theory
10 editions published between 2007 and 2011 in English and held by 558 WorldCat member libraries worldwide
The main topics of the book are the critical values of Dirichlet Lfunctions and Hecke Lfunctions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet Lfunctions, all previous papers and books reiterate a single old result with a single old method. After a review of elementary Fourier analysis, the author presents completely new results with new methods, though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications, new formulas for the second factor of the class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge of modular forms. However, all definitions and facts are clearly stated, and precise references are given. The notion of nearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke Lfunctions of an imaginary quadratic field. Other notable features of the book are: (1) some new results on classical Eisenstein series; (2) the discussion of isomorphism classes of elliptic curves with complex multiplication in connection with their zeta function and periods; (3) a new class of holomorphic differential operators that send modular forms to those of a different weight. The book will be of interest to graduate students and researchers who are interested in special values of Lfunctions, class number formulae, arithmetic properties of modular forms (especially their values), and the arithmetic properties of Dirichlet series. It treats in detail, from an elementary viewpoint, the simplest cases of a fundamental area of ongoing research, the only prerequisite being a basic course in algebraic number theory
Automorphic functions and number theory
by
Gorō Shimura(
Book
)
8 editions published in 1968 in English and held by 536 WorldCat member libraries worldwide
8 editions published in 1968 in English and held by 536 WorldCat member libraries worldwide
Introduction to the arithmetic theory of automorphic functions
by
Gorō Shimura(
Book
)
26 editions published between 1971 and 1994 in English and Undetermined and held by 494 WorldCat member libraries worldwide
26 editions published between 1971 and 1994 in English and Undetermined and held by 494 WorldCat member libraries worldwide
Arithmetic of quadratic forms
by
Gorō Shimura(
)
9 editions published in 2010 in English and Undetermined and held by 419 WorldCat member libraries worldwide
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case
9 editions published in 2010 in English and Undetermined and held by 419 WorldCat member libraries worldwide
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case
Modular forms basics and beyond
by
Gorō Shimura(
)
8 editions published in 2012 in English and held by 388 WorldCat member libraries worldwide
This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows thebasics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of halfintegral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes: (I) The correspondence between the forms of halfintegral weight and those of integral weight. (II) The arithmeticity of various Dirichlet series associated with modular forms of integral or halfintegral weight. Goro Shimura is currently a professor emeritus of mathematics at Princeton University
8 editions published in 2012 in English and held by 388 WorldCat member libraries worldwide
This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows thebasics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of halfintegral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes: (I) The correspondence between the forms of halfintegral weight and those of integral weight. (II) The arithmeticity of various Dirichlet series associated with modular forms of integral or halfintegral weight. Goro Shimura is currently a professor emeritus of mathematics at Princeton University
Abelian varieties with complex multiplication and modular functions
by
Gorō Shimura(
Book
)
5 editions published between 1997 and 1998 in English and held by 337 WorldCat member libraries worldwide
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
5 editions published between 1997 and 1998 in English and held by 337 WorldCat member libraries worldwide
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
Arithmetic and analytic theories of quadratic forms and Clifford groups
by
Gorō Shimura(
Book
)
6 editions published in 2004 in English and held by 302 WorldCat member libraries worldwide
6 editions published in 2004 in English and held by 302 WorldCat member libraries worldwide
Arithmeticity in the theory of automorphic forms
by
Gorō Shimura(
Book
)
7 editions published in 2000 in English and held by 302 WorldCat member libraries worldwide
7 editions published in 2000 in English and held by 302 WorldCat member libraries worldwide
Euler products and Eisenstein series
by
Gorō Shimura(
Book
)
4 editions published in 1997 in English and held by 282 WorldCat member libraries worldwide
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
4 editions published in 1997 in English and held by 282 WorldCat member libraries worldwide
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
Complex multiplication of Abelian varieties and its applications to number theory
by
Gorō Shimura(
Book
)
7 editions published between 1961 and 1975 in English and held by 218 WorldCat member libraries worldwide
7 editions published between 1961 and 1975 in English and held by 218 WorldCat member libraries worldwide
Collected papers
by
Gorō Shimura(
Book
)
4 editions published in 2002 in English and held by 128 WorldCat member libraries worldwide
4 editions published in 2002 in English and held by 128 WorldCat member libraries worldwide
Geometry and number theory : a volume in honor of André Weil
(
Book
)
3 editions published in 1983 in English and held by 109 WorldCat member libraries worldwide
3 editions published in 1983 in English and held by 109 WorldCat member libraries worldwide
Collected papers
by
Gorō Shimura(
Book
)
6 editions published between 2003 and 2011 in English and held by 26 WorldCat member libraries worldwide
6 editions published between 2003 and 2011 in English and held by 26 WorldCat member libraries worldwide
The map of my life
by
Gorō Shimura(
Book
)
5 editions published in 2008 in English and held by 24 WorldCat member libraries worldwide
Tells about the author's life, beginning with his earliest childhood days. This book describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a postwar university system that was seriously deficient, and his life as a mathematician in Princeton and in the international academic community
5 editions published in 2008 in English and held by 24 WorldCat member libraries worldwide
Tells about the author's life, beginning with his earliest childhood days. This book describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a postwar university system that was seriously deficient, and his life as a mathematician in Princeton and in the international academic community
On the Fourier coefficients of modular forms of several variables
by
Gorō Shimura(
Book
)
1 edition published in 1975 in English and held by 24 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 24 WorldCat member libraries worldwide
Collected papers
by
Gorō Shimura(
Book
)
6 editions published in 2003 in English and held by 22 WorldCat member libraries worldwide
6 editions published in 2003 in English and held by 22 WorldCat member libraries worldwide
Collected papers
by
Gorō Shimura(
)
2 editions published in 2002 in English and held by 16 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 16 WorldCat member libraries worldwide
Collected papers
by
Gorō Shimura(
)
2 editions published in 2002 in English and held by 16 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 16 WorldCat member libraries worldwide
Collected papers : 19541966
by
Gorō Shimura(
Book
)
1 edition published in 2002 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 14 WorldCat member libraries worldwide
Collected papers : 19781988
by
Gorō Shimura(
Book
)
1 edition published in 2003 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 14 WorldCat member libraries worldwide
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Associated Subjects
Abelian varieties Algebra Algebraic number theory Automorphic forms Automorphic functions Dirichlet series Eisenstein series Euler products Forms, Modular Forms, Quadratic Fourier series Functions, Theta Geometry Geometry, Algebraic Japan Lfunctions Linear algebraic groups Mathematicians Mathematics Modular functions Number theory Numerical analysis
Alternative Names
Goro Shimura.
Shimura, G. 1930
Shimura, Goro
Shimura, Goro 1930
Šimura, Goro.
シムラ, ゴロウ
志村五郎 1930
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