Number Theory A Seminar held at the Graduate School and University C
This is the third Lecture Notes volume to be produced in the framework of the New York Number Theory Seminar. The papers contained here are mainly research papers. N
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1240
Number Theory A Seminar held at the Graduate School and University Center of the City University of New York 1984-85
Edited by O.V. Chudnovsky, G. V. Chudnovsky, H. Cohn and M.B. Nathanson
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann
1240
Number Theory A Seminar held at the Graduate School and University Center of the City University of New York 1984-85
Edited by O.V. Chudnovsky, G. V. Chudnovsky, H. Cohn and M.B. Nathanson
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
David V. Chudnovsky Gregory V. Chudnovsky Department of Mathematics, Columbia University NewYork, NY 10027, USA Harvey Cohn Department of Mathematics, (C.U.N.Y.) City College NewYork, NY 10031, USA Melvyn B. Nathanson Office of the Provostand Vice President for AcademicAffairs Lehman College (C.U.N.Y.) Bronx, NY 10468, USA
Mathematics Subject Classification (1980): 10-06 ISBN 3-540-17669-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17669-1 Springer-Verlag New YorkBerlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergslr. 2146/3140-543210
INTRODUCTION Th i sis the th i rd vo 1ume or papers presented at the New York Number Theory Seminar.
Since 1982 the Seminar has been meeting
every Tuesday afternoon during the academic year at trle Graduate School and University Center of the City University of New York. Tile goa 1 or the Sem i nar is to prov i de a f o r urn for the exposure or new results In number theory and a1 1 ied rields in the New York met ropo 1 i tan ar-e a,
Mathemat i clans who p 1an to be in New Yor k and
would like to attend or lecture In the Seminar are encouraged to contact the organizers.
TABLE OF CONTENTS D.V. CHUDNOVSf of this polygon, one has to construct only the
power series expansion of Y(x;x the evaluation of Y(x;x in a given precision.
i)
with sufficiently many terms so that
at x x + be close to the actual one withi) i l From the point of view of minimal complexity
the main problem is to determine the minimal number of m + 2 points xi and their positions, for which the number of operations necessary to complete the analytic continuation within a given precision is minimal. This leads to an interesting extremal problem which we solve ly below in a few most important cases, e.g. when circle (the only two basic elements needed).
is a line or a
y
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