志村五郎数学論文集（全4巻）Shimura: Collected Papers, 4 Vols.

G. Shimura: Collected Papers, 4 Vols.

Goro Shimura, Princeton University, Princeton, NJ, USA (Ed.)

2002年8月-10月出版予定　全4巻／約3,354頁　ハードカバー　セット概価￥121,720

代数学や整数論分野で多大な貢献をしているプリンストン大学教授、志村五郎氏の論文集（全4巻）が近く出版の予定である。特に、算術幾何学と関数の保形形式に関する研究は、志村教授の重要な研究成果を結集したライフワークであり、関連分野の研究者によって高く評価されている。本書は、全4巻より構成されており、1954年から現在までの最も重要な論文103編が収録されている。アーベル多様体の代数幾何学的理論の拡張、多元環のゼータ関数、ヘッケの作用素によるゼータ関数、ハッセのゼータ関数、保形関数論と整数論、代数体上の代数群の研究、代数多様体、離散部分群の数論的研究、保形関数におけるラマヌジャン-ペーターソンの予想、ジーゲルのモジュラ関数、保形関数の整数論的・代数幾何学的研究などの成果が扱われている。また、収載各論文は未修正であるが、各巻の末尾で著者によるノートが付されている。また、著者は第1巻における若干の訂正に対して、「正誤表」を挿入しており、頁数・文字・記号などの落丁や不鮮明箇所には訂正が加えられている。志村教授は、1996年に、アメリカ数学会よりSteele Prize賞を、算術幾何学と関数の保形形式の研究により受賞している。今回の論文集の刊行は、志村教授の偉業をかざるにふさわしい企画である。

各巻の詳細は下記のとおり。

Volume 1: 1954 - 1966

2002年8月出版予定　808頁　ハードカバー　予価￥30,080　ISBN 0-387-95406-6

Contents: Preface.- The articles included in this collection.- List of articles.- A note on the normalization-theorem of an integral domain.- Reduction of algebraic varieties with respect to a discrete valuation of the basic field.- On complex multiplications.- La fonction [zeta] du corps des fonctions modulaires elliptiques.- Correspondences modulaires et les fonctions zeta de courbes algebriques.- Modules des varietes abeliennes polarisees et fonctions modulaires.- Functions automorphes et correspondances modulaires.- On the theory of automophic functions.- Sur les integrales attachees aux formes automorphes.- On specializations of abelian varieties (with Shoji Koizumi).- On vector differential forms attached to automorphic forms (with Michio Kuga).- On the zeta functions of the algebraic curves uniformized by certain automorphic functions.- On Dirichlet series and abelian varieties attached to automorphic forms.- On the class-fields obtained by complex multiplication of abelian varieties.- Arithmetic of alternating forms and quaternion hermitian forms.- On analytic families of polarized abelian varieties and automorphic functions.- On the cohomology groups attached to certain vector valued differential forms on the product of the upper half planes.

Volume 2: 1967 - 1977

2002年8月出版予定　848頁　ハードカバー　予価￥30,080　ISBN 0-387-95416-3

Contents: List of Articles.- Discontinuous groups and abelian varieties.- Construction of class fields and zeta functions of algebraic curves.- Number fields and zeta functions associated with discontinuous groups and algebraic varieties.- Algebraic number fields and symplectic discountinuous groups.- Algebraic varieties without deformation and the Chow variety.- An l-adic method in the theory of automorphic forms.- Local representations of Galois groups.- On canonical models of arithmetic quotients of bounded symmetric domains.- On canonical models of arithmetic quotients of bounded symmetric domains: II.- On arithmetic automorphic functions.- On the zeta-function of an abelian variety with complex multiplication.- Class fields over real quadratic fields in the theory of modular functions.- On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields.- On the field of rationality for an abelian variety.- Class fields over real quadratic fields and Hecke operators.- On modular forms of half integral weight.- On the factors of the jacobian variety of a modular function field.- On the trace formula for Hecke operators.- On the holomorphy of certain Dirichlet series.- On the real points of an arithmetic quotient of a bounded.

Volume 3: 1978 - 1988

2002年9月出版予定　936頁　ハードカバー　予価￥31,860　ISBN 0-387-95417-1

Contents: List of articles.- On certain reciprocity-laws for theta functions and modular forms.- The arithmetic of automorphic forms with respect to a unitary group.- The special values of the zeta functions associated with Hilbert modular forms.- Automorphic forms and the periods of abelian varieties.- On some problems of algebraicity.- The arithmetic of certain zeta functions and automorphic forms on orthogonal groups.- The critical values of certain zeta functions associated with modular forms of half-integral weight.- On certain zeta functions attached to two Hilbert modular forms: I. The case of Hecke characters.- On certain zeta functions attached to two Hilbert modular forms: II. The case of automorphic forms on a quaternion algebra.- Arithmetic of differential operators on symmetric domains.- Models of an abelian variety with complex multiplication over small fields.- The periods of certain automorphic forms of arithmetic type.- Confluent hypergeometric functions on tube domains.- Algebraic relations between critical values of zeta functions and inner products.- On Eisenstein series.- Differential operators and the singular values of Eisenstein series.- On differential operators attached to certain representations of classical groups.

Volume 4: 1989 - 2001

2002年10月出版予定　762頁　ハードカバー　予価未定　ISBN 0-387-95418-X

Contents: List of articles.- Yutaka Taniyama and his time.- L-functions and eigenvalue problems.- Invariant differential operators on hermitian symmetric spaces.- On the fundamental periods of automorphic forms of arithmetic type.- The critical values of certain Dirichlet series attached to Hilbert modular forms.- On the transformation formulas of theta series.- On the Fourier coefficients of Hilbert modular forms of half-integral weight.- Fractional and trigonometric expressions for matrices.- Euler products and Fourier coefficients of automorphic forms on symplectic groups.- Differential operators, holomorphic projection, and singular forms.- Eisenstein series and zeta functions on symplectic.- Zeta functions and Eisenstein series on metaplectic groups.- Convergence of zeta functions on symplectic and metaplectic groups.- Response.- Zeta functions and Eisenstein series on classical groups.- An exact mass formula for orthogonal groups.- The number of representations of an integer by a quadratic form.- Genera