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MATH FILE -Mathematical Reviews Online Notices of the American Mathematical Society November 1984, Issue 237 Volume 31 , Number 7, Pages 737- 840 Providence, Rhode Island ·USA JSSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet­ ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the o(fice of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. MEETING# DATE PLACE ABSTRACT DEADLINE ISSUE 816 January 9-13, 1985 Anaheim, California EXPIRED January (91st Annual Meeting) 817 March 22-23, 1985 Chicago, Illinois January 23 March 818 April 12-13, 1985 Tucson, Arizona January 25 March 819 April 20-21, 1985 Worcester, Massachusetts January 28 March 820 May 3-4, 1985 Mobile, Alabama January 30 March 821 August 12-15, 1985 Laramie, Wyoming (89th Summer Meeting) October 26-27, 1985 Amherst, Massachusetts November 1-2, 1985 Columbia, Missouri January 7-11, 1986 iNew Orleans, Louisiana (92nd Annual Meeting) January 21-25, 1987 San Antonio, Texas (93rd Annual Meeting) January 6-11, 1988 Atlanta, Georgia (94th Annual Meeting) August 8-12, 1988 Providence, Rhode Island (AMS Centennial Celebration l DEADLINES: Advertising Uanuary 1985 Issue) November 15, 1984 (March 1985 Issue) February 7, 1985 News/Special Meetings Uanuary 1985 Issue) October 29, 1984 (March 1985 Issue) january 25, 1985 Other Events Sponsored by the Society January 7-8, 1985, AMS Short Course: Fair Allocation, Anaheim, California. May 1985, Symposium on Some Mathematical Questions in Biology, Plant Biology, Los Angeles, California. June 23-August 31, 1985, Joint Summer Research Conferences in the Mathematical Sciences, Humboldt State University, Arcata, California. June 30-July 13, 1985, AMS-SIAM Summer Seminar on Reacting Flows: Combustion and Chemical Re­ actors, Cornell University, Ithaca, New York. July 8-26, 1985, AMS Summer Research Institute on Algebraic Geometry, Bowdoin College, Brunswick, Maine. Substribers' changa of address should be reported well in advance to avoid disruption of service: address labels are prepared four to six -ks in advance of the date of mailing. Requests for a change of address should always include the member or subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postel Service change-of­ address forms are not adequate for this purpose, since they make no provision for several important items of information which are essential for the AMS records. Suitable forms are published from time to time in the Notices (e.g. June 198•, page 421). Send change of address notices to the Society at Post Office Box 6248, Providence, RI 02~0. (Notices is published eight times a year (January, February, April, June, August, October, November, December) by the American Mathematical Society at 201 Charles Street, Providence, RI 02904. Second class postage paid at Providence, RI and additional mailing offices. POSTMASTER: Send address change notices to Membership and Sales Department, American Mathematical Society, Post Office Box 6248, Providence, RI 02~0.] Publication here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. The street address should never be used by correspondents, unless they plan to deliver their messaga by hand. Members ara strongly urged to notify the Society themselves of address changes (in the manner described above), since (as explained above) reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society Volume 31, Number 7, November 1984 EDITORIAL COMMITTEE Paul F. Baum, Ralph P. Boas Raymond L. johnson, Mary Ellen Rudin Bertram Walsh, Daniel Zelinsky 739 L-Series of Elliptic Curves, the Birch-Swinnerton­ Everett Pitcher (Chairman) Dyer Conjecture, and the Class Number Problem of MANAGING EDITOR Gauss, Lincoln K. Durst D. Zagier ASSOCIATE EDITORS 744 28th Annual AMS Survey Hans Samelson, Queries Ronald L. Graham, Special Articles Faculty Salaries, Tenure, Women, 744 SUBSCRIPTION INFORMATION Salaries of New Doctorates, 749 Subscription prices for Volume 31 (1984) 1984 Survey of New Doctorates, 754 are $50 list; $25 member. (The subscrip· Doctoral Degrees Conferred in 1983-1984, 757 tion price for members is included in the (1982-1983 Supplement, 770} annual dues.) A late charge of 10% of the subscription price will be imposed upon 771 Mathematics Salaries: Up and Competitive, orders received from nonmembers after R. D. Anderson january 1 of the subscription year. Sub­ 772 Mathematics and Technology, scribers outside the United States and India must pay a postage surcharge of Robert Hermann $5; subscribers in India must pay a 774 News and Announcements postage surcharge of $15. Subscrip- 778 Letters to the Editor tions and orders for AMS publications should be addressed to the American 783 NSF News & Reports Mathematical Society, P.O. Box 1571, 784 Queries Annex Station, Providence, Rl 02901. All orders must be prepaid. 786 AMS Elections of 1984 787 Future Meetings of the Society ORDERS FOR AMS BOOKS AND INQUIRIES ABOUT SALES, SUBSCRIP­ Anaheim, january 9-73, 787 TIONS, AND DUES may be made by Chicago, March 22-23, 790 calling Carol-Ann Blackwood at Tucson, April 72-73, 791 800-556-7774 (toll free in U.S.) between Worcester, April 20-27, 793 8:00a.m. and 4:15p.m. eastern time, Monday through Friday. Tucson, May 3-4, 795 Invited Speakers and Special Sessions, 796 INFORMATION ABOUT ADVERTISING 798 Joint Summer Research Conference Series in the Notices may be obtained from Wahlene Siconio at 401-272-9500. 799 1985 AMS-SIAM Summer Seminar CORRESPONDENCE, including changes 800 Special Meetings of address should be sent to American 804 New AMS Publications Mathematical Society, P.O. Box 6248, 806 Miscellaneous Providence, Rl 02940. Personal Items, 806; Deaths, 806; Second class postage paid at Providence, Rl, and additional mailing Visiting Mathematicians (Supplement}, 806; offices. Copyright © 1984 by the Application Deadlines, 807 American Mathematical Society. 809 Advertisements Printed in the United States of America. 834 Preregistration Forms The paper used in this journal is acid-free and falls within the guidelines established Employment Register, 834, 835, 836 to ensure permanence and durability. Anaheim Preregistration and Housing, 837, 838 The following article is the eighth in the series of Special Articles published in the Notices. Its author, DoN ZAGIER, studied at M.I.T. as an undergraduate (B.S. in mathematics and B.S. in physics, in 1968) and did graduate work at Oxford (D.Phil., 1972) where he worked with Atiyah and Hirzebruch. Since that time he has worked at Bonn, ETH (Zurich), IHES (Bures-sur-Yvette) and Harvard. Since 1979 he has been a professor at the University of Maryland; he is also a member of the Max Planck Institute for Mathematics in Bonn. His primary research interests are number theory and the theory of modular forms. The series of Special Articles was created to provide a place for articles on mathematical subjects of interest to the general membership of the Society. The Editorial Committee of the Notices is especially interested in the quality of exposition and intends to maintain the highest standards in order to assure that the Special Articles will be accessible to mathematicians in all fields. The articles must be interesting and mathematically sound. They are first refereed for accuracy and (if approved) accepted or rejected on the basis of the breadth of their appeal to the general mathematical public. Items for this series are solicited and, if accepted, will be paid for at the rate of $250 per page up to a maximum of $750. Manuscripts to be considered for this series should be sent to Ronald L. Graham, Associate Editor for Special Articles, Notices of the American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940. L-Series of Elliptic Curves, the Birch-Swinnerton-Dyer Conjecture, and the Class Number Problem of Gauss by D. Zagier 1. Elliptic curves over Q. Consider a Diophan­ these agree. It is known exactly what groups 1 tine equation in two variables, i.e., a polynomial can occur: 1 has the structure Z/(2n-1)Z, Z/2nZ, equation f(x, y) = 0 with rational coefficients or Z/2Z X Z/2nZ for some n EN, depending on which we want to solve in rational numbers. whether 4x3 - ax- b in (1) has 0, 1, or 3 rational Already in the works of Diophantus it is clear roots (this is elementary), and a deep theorem of that the level of difficulty of this problem is Mazur (1977) says that n is then ~ 5, ~ 6, or ~ 4, very different for different classes of polynomials respectively, all fifteen cases occurring infinitely f.
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