Collected Papers: Volume II 1967–1977

845 Pages·2002·36.591 MB·English

by  Goro Shimura (auth.)

Collected Papers
Volume II
Springer
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Goro Shimura
Collected Papers
Volume II
1967-1977
Springer
Goro Shimura
Mathematics Department
Princeton University
Princeton, NJ 08544-\ 000
USA
Library of Congress Cataloging-in-Publication Data
Shimura, Goro, 1930-
[Papers, Selections 1
Collected papers.
p. cm.
Includes bibliographical references and index.
ISBN-13:978-1-4612-7405-6 e-ISBN-13:978-1-4612-2076-3
001: 10.1007/978-1-4612-2076-3
I. Number theory. 2. Automorphic functions. J. Title.
QA3 .S547 2002
5 I O--dc2 I 2001057678
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Contents
List of Articles vii
[67a] Discontinuous groups and abelian varieties
[67b] Construction of class fields and zeta functions of algebraic curves 30
[67c] Number fields and zeta functions associated with discontinuous groups
and algebraic varieties . . . . . . . . . . . . . . . . . . . . . 132
[67d] Algebraic number fields and symplectic discontinuous groups 141
[68a] Algebraic varieties without deformation and the Chow variety 231
[68c] An f-adic method in the theory of automorphic forms. 237
[69] Local representations of Galois groups ........ . 273
[70a] On canonical models of arithmetic quotients of bounded symmetric
domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
[70b] On canonical models of arithmetic quotients of bounded symmetric
domains: II . . . . . . . . . . . . . . 378
[71a] On arithmetic automorphic functions 400
[7Ib] On the zeta-function of an abelian variety with complex multiplication. 406
[7Ic] Class fields over real quadratic fields in the theory of modular functions 436
[7Ie] On elliptic curves with complex mUltiplication as factors ofthe lacobians
of modular function fields . . . . . . . . . . . 449
[72a] On the field of rationality for an abelian variety 459
vi Contents
[72b] Class fields over real quadratic fields and Heeke operators 471
[73a] On modular forms of half integral weight . . . . . . . . . 532
[73d] On the factors of the jacobian variety of a modular function field . 574
[74] On the trace formula for Heeke operators .. 596
[75a] On the holomorphy of certain Dirichlet series 633
[75b] On the real points of an arithmetic quotient of a bounded symmetric
domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 653
[75c] On some arithmetic properties of modular forms of one and several
variables .............................. 683
[75d] On the Fourier coefficients of modular forms of several variables . 708
[76a] Theta functions with complex multiplication ........... 716
[76b] The special values of the zeta functions associated with cusp forms 740
[77a] On abelian varieties with complex multiplication 762
[77b1 Unitary groups and theta functions . . . . . . . . 784
[77c 1 On the derivatives of theta functions and modular forms 790
[77d] On the periods of modular forms . . 813
Notes II 825
List of Articles
The numbers in parentheses are the articles not included in this collection.
Volume I
[(52)] On a certain ideal of the center of a Frobeniusean algebra, Scientific Papers of
the College of General Education, University ofTokyo, 2 (1952),117-124.
[54] A note on the normalization-theorem of an integral domain, Scientific Papers of
the College ofG~neral Education, University of Tokyo, 4 (1954), I-S.
[55] Reduction of algebraic varieties with respect to a discrete valuation of the basic
field, American Journal of Mathematics, 77 (1955), 134-176.
[56] On complex multiplications, Proceedings of the International Symposium on Al
gebraic Number Theory, Tokyo-Nikko, 1955, Science Council of Japan, Tokyo
(1956), 23-30.
[57a] La fonction ~ du corps des fonctions modulaires elliptiques, Comptes rendus
des seances de l' Academie des Sciences, 244 (1957), 2127-2130.
[(57b)] Kindai-teki Seisu-ron (Modem Number Theory, in Japanese, with Yutaka
Taniyama), Kyoritsu Shuppan, 1957.
[5Sa] Correspondances modulaires et les fonctions zeta de courbes algebriques,
Journal of the Mathematical Society of Japan, 10 (195S), 1-28.
[58b] Modules des varietes abeliennes polarisees et fonctions modulaires, Seminaire
Henri Cartan, Ecole Normale Superieure, 1957/58, Fonctions Automorphes,
Expose 18-20 (195S).
[(5Sc)] Fonctions automorphes et varietes abeliennes, Seminaire Bourbaki, 1957/58,
Expose 167 (195S).
viii List of Articles
[59a] Fonctions automorphes et correspondances modulaires, Proceedings of the
International Congress of Mathematicians, Edinburgh, 1958 (1959), 330-338.
[59b] On the theory of automorphic functions, Annals of Mathematics, 70 (1959),
101-144.
[59c] Sur les integrales attachees aux formes automorphes, Journal of the Mathemat
ical Society ofJapan, 11 (1959),291-311.
[59d] On specializations of abelian varieties (with Shoji Koizumi), Scientific Papers
of the College of General Education, University of Tokyo, 9 (1959), 187-21l.
[60a] On vector differential forms attached to automorphic forms (with Michio Kuga),
Journal of the Mathematical Society of Japan, 12 (1960), 258-270.
[(60b)] Automorphic functions and number theory: I (in Japanese), Sugaku, 11 (1960),
193-205.
[(61a)] Complex multiplication of abelian varieties and its applications to number theory
(with Yutaka Taniyama), Publications of the Mathematical Society of Japan,
No.6 (1961).
[61 b] On the zeta functions of the algebraic curves uniformized by certain automorphic
functions, Journal of the Mathematical Society of Japan, 13 (1961), 275-33l.
[(61 c)] Automorphic functions and number theory: II (in Japanese), Sugaku, 13 (1961),
65-80.
[62a] On Dirichlet series and abelian varieties attached to automorphic forms, Annals
of Mathematics, 76 (1962), 237-294.
[62b] On the class-fields obtained by complex multiplication of abelian varieties,
Osaka Mathematical Journal, 14 (1962), 33-44.
[63a] Arithmetic of alternating forms and quaternion hermitian forms, Journal of the
Mathematical Society of Japan, 15 (1963), 33-65.
[63b] On analytic families of polarized abelian varieties and automorphic functions,
Annals of Mathematics, 78 (1963),149-192.
[63c] On the cohomology groups attached to certain vector valued differential forms
on the product of the upper half planes (with Yozo Matsushima), Annals of
Mathematics, 78 (1963), 417-449.
[63d] On modular correspondences for Sp(n, Z) and their congruence relations,
Proceedings of the National Academy of Sciences, 49 (1963),824-828.
[63e] On the fields of definition for fields of automorphic functions, Proceedings of
the 1963 Number Theory Conference, Boulder, Colorado, August 5-24, 1963,
26-32.
[64a] Arithmetic of unitary groups, Annals of Mathematics, 79 (1964), 369-409.
[64b] On the field of definition for a field of automorphic functions, Annals of
Mathematics, 80 (1964), 160-189.
List of Articles ix
[64c] Class-fields and automorphic functions, Annals of Mathematics, 80 (1964),444-
463.
[64d] On purely transcendental fields of automorphic functions of several variables,
Osaka Joumal of Mathematics, 1 (1964),1-14.
[64e] The zeta function of an algebraic variety and automorphic functions, Summer
Research Institute on Algebraic Geometry, Woods Hole, Massachusetts, July
6-31, 1964 (mimeographed notes of lectures).
[65a] On the field of definition for a field of automorphic functions: II, Annals of
Mathematics,81 (1965), 124-165.
[65b] On the zeta function of a fibre variety whose fibres are abelian varieties (with
Michio Kuga), Annals of Mathematics, 82 (1965), 478-539.
[66a] A reciprocity law in non-solvable extensions, Journal fUr die reine und
angewandte Mathematik, 221 (1966),209-220.
[66b] Moduli and fibre systems of abelian varieties, Annals of Mathematics, 83 (1966),
294-338.
[66c] On the field of definition for a field of automorphic functions: III, Annals of
Mathematics, 83 (1966),377-385.
[66d] Moduli of abelian varieties and number theory, Proceedings of the Symposium
on Pure Mathematics, 9, Algebraic groups and discontinuous subgroups, 1965,
American Mathematical Society, (1966), 312-332.
VolumeD
[67a] Discontinuous groups and abelian varieties, Mathematische Annalen, 168
(1967), 171-199.
[67b] Construction of class fields and zeta functions of algebraic curves, Annals of
Mathematics, 85 (1967), 58-159.
[67c] Number fields and zeta functions associated with discontinuous groups and al
gebraic varieties, Proceedings of the International Congress of Mathematicians,
Moscow, 1966, 100-107 (1967).
[67d] Algebraic number fields and symplectic discontinuous groups, Annals of
Mathematics, 86 (1967), 503-592.
[68a] Algebraic varieties without deformation and the Chow variety, Journal of the
Mathematical Society of Japan, 20 (1968),336-341.
[(68b)] Automorphic functions and number theory, Lecture notes in mathematics 54,
Springer, 1968.
[68c] An e-adic method in the theory of automorphic forms, the text of a lecture
at the conference Automorphic functions for arithmetically defined groups,
Oberwolfach, Germany, July 28-August 3,1968.