Collected Papers: Volume III: 1978-1988

939 Pages·2003·120.94 MB·English

by  Goro Shimura (auth.)

Collected Papers
Volume III
Springer
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Tokyo
Goro Shimura
Collected Papers
Volume III
1978-1988
Springer
Goro Shimura
Mathematics Department
Princeton University
Princeton, NJ 08544-1000
USA
Library of Congress Cataloging-in-Publication Data
Shimura, Goro, 1930-
[Papers, Selections)
Collected papers.
p. cm.
Includes bibliographical references and index.
Contents:v. l.1954-1966-v.2. 1967-1977-v.3. 1978-1988-v.4. I 989-200l.
ISBN-13:978-1-461Z-7398-1 e-ISBN-13:978-1-461Z-Z060-Z
DO [: 1O.1007/978-1-4612-2060-Z
I. Number theory. 2. Automorphic functions. I. Title.
QA3 .S547 2002
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Contents
List of Articles vii
[78a] On certain reciprocity-laws for theta functions and modular forms . . 1
[78b] The arithmetic of automorphic forms with respect to a unitary group . 38
[78c] The special values of the zeta functions associated with Hilbert
modular forms . . . . . . . . . . . . . . . . . . . . . . 75
[79a] Automorphic forms and the periods of abelian varieties. . . . . . 115
[79b] On some problems of algebraicity . . . . . . . . . . . . . . . . . 147
[80] The arithmetic of certain zeta functions and automorphic forms on
orthogonal groups .......................... 154
[81a] The critical values of certain zeta functions associated with modular
forms of half-integral weight . . . . . . . . . . . . . . . . . . . . 217
[8Ib] On certain zeta functions attached to two Hilbert modular forms:
I. The case of Hecke characters .................. 241
[8Ic] On certain zeta functions attached to two Hilbert modular forms:
II. The case of automorphic forms on a quatemion algebra . . . 279
[8Id] Arithmetic of differential operators on symmetric domains ... 318
[82a] Models of an abelian variety with complex multiplication over
small field!. . . . . . . . . . . . . . . . . . . . . . . . . . . 349
[82b] The periods of certain automorphic forms of arithmetic type .. 360
[82c] Confluent hypergeometric functions on tube domains . . . . . . 388
[83a] Algebraic relations between critical values of zeta functions and
inner products. . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
[83b] On Eisenstein series ........................ 455
[84a] Differential operators and the singular values of Eisenstein series 515
[84b] On differential operators attached to certain representations of
classical groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 584
vi Contents
[85a] On Eisenstein series of half-integral weight 610
[85b] On the Eisenstein series of Hilbert modular groups . 644
[86] On a class of nearly holomorphic automorphic forms 686
[87a] Nearly holomorphic functions on hermitian symmetric spaces 746
[87b] On Hilbert modular forms of half-integral weight . . . . . . . 774
[88] On the critical values of certain Dirichlet series and the periods of
automorphic forms . . . . . . . . . . . . . . . . . . . . . . . . . . 848
Notes II 909
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 of Tokyo, 2 (1952), 117-124.
[54] A note on the normalization-theorem of an integral domain, Scientific Papers of
the College of General Education, University of Tokyo, 4 (1954),1-8.
[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 ofthe International Symposium on Al
gebraic Number Theory, Tokyo-Nikko, 1955, Science Council of Japan, Tokyo
(1956), 23-30.
[57a] La fonction t; 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.
[58a] Correspondances modulaires et les fonctions zeta de courbes algebriques,
Journal of the Mathematical Society of Japan, 10 (1958),1-28.
[58b] Modules des varietes abeliennes polarisees et fonctions modulaires, Seminaire
Henri Cartan, Ecole Norrnale Superieure, 1957/58, Fonctions Automorphes,
Expose 18-20 (1958).
[(58c)] Fonctions automorphes et varietes abeliennes, Seminaire Bourbaki, 1957/58,
Expose 167 (1958).
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), 187-211.
[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.
[( 61 a)] 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 ofthe Mathematical Society of Japan, 13 (1961), 275-331.
[(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 Journal 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.
Volume II
[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 l-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.