Collected Papers I: 1954 - 1966

ISBN-13: 9781493918096 / Angielski / Miękka / 2014 / 795 str.

Goro Shimura

Opis

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement for his "important and extensive work on arithmetical geometry and automorphic forms." His seminal work has resulted in the "many notations in number theory that carry his name and that have long been familiar to workers in the field." These 4 volumes contain 103 of his most important papers, beginning in 1954 and continuing up through the present.

Recenzje

From the reviews:

"This book is the first in a row of four announced volumes. It covers the period 1954-1966 during which Goro Shimura produced more than thirty publications. ... Important contributions concerning the zeta function of an algebraic variety and automorphic functions are featured. ... the mimeographed 1964 lecture notes by Shimura appear in a final form. They are completed by fascinating historical notes and comments made by the author ... ." (Jean-Paul Pier, Zentralblatt MATH, Vol. 1008, 2003)

Spis treści

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 * Correspondances modulaires et les fonctions zeta de courbes algébriques * Modules des variétés abéliennes polarisées et fonctions modulairés * Fonctions automorphes et correspondances modulaires * On the theory of automorphic functions * Sur les intégrales attachées 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 (with Yozo Matsushima) * On modular correspondences for Sp(n, Z) and their congruence relations * On the fields of definition for fields of automorphic functions * Arithmetic of unitary groups * On the field of definition for a field of automorphic functions * Class-fields and automorphic functions * On purely transcendental fields of automorphic functions of several variables * The zeta function of an algebraic variety and automorphic functions * On the field of definition for a field of automorphic functions: II * On the zeta function of a fibre variety whose fibres are abelian varieties (with Michio Kuga) * A reciprocity law in non-solvable extensions * Moduli and fibre systems of abelian varieties * On the field of definition for a field of automorphic functions: III * Moduli of abelian varieties and number theory * Notes