Number Theory in Progress

Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997

Bearbeitet von Kálmán Györy, Henryk Iwaniec, Jerzy Urbanowicz

Reprint 2012 1999. Buch. XXII, 1207 S. Hardcover ISBN 978 3 11 015715 4 Gewicht: 2231 g

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These are the Proceedings of the International Conference on Number Theory held in Zakopane-Ko´scielisko, Poland, from June 30 to July 9, 1997. The conference was organized by the Stefan Banach International Mathematical Center to celebrate the 60th birthday of Professor Andrzej Schinzel. Andrzej Schinzel is the editor-in-chief of Acta Arithmetica—the first interna- tional journal devoted exclusively to number theory—for over 28 years. He is also well known for many original results in various areas of number theory appearing in nearly 200 research papers. His main contributions are described in the article of W ladys law Narkiewicz in these Proceedings. About 130 mathematicians from 21 countries attended the conference. The focus of the meeting was twofold: Diophantine Problems and Polynomials, and Elementary and Analytic Number Theory. Bogdan Bojarski, Director of the Insti- tute of Mathematics of the Polish Academy of Sciences opened the conference with an address to the participants, and Wladys law Narkiewicz delivered the opening lecture on selected works of Andrzej Schinzel. The scientific program was supple- mented by a banquet and a one-day excursion, to Cracow, the former capital of Poland. After the excursion, Andrzej Schinzel presented a requested lecture on the history of Poland—a subject which is close to his heart. The Proceedings contain 71 selected, refereed research and survey papers by conference speakers and a few invited mathematicians who were unable to come to the conference. The material is divided into two volumes according to the confer- ence subjects. The articles of the first volume are concerned with diophantine problems and polynomials (diophantine equations, diophantine approximation, transcendental number theory and polynomials). The second volume contains the papers related to elementary and analytic number theory (sieve methods, modular and automorphic forms, Hecke operators, estimates on exponential and character sums, zeta functions and L-functions). A noteworthy feature of these volumes is the large number of papers written by leading mathematicians. Most of the con- tributions are in English while a few are in French. We thank all the authors and referees for all their contributions to the Proceedings. Many people helped in the organization of the conference or in the editing of the Proceedings. Special thanks are due to Bogdan Bojarski for his guidance and help. We also thank Robert Tijdeman, who played an important role from the initial planning of the conference to the publication of the Proceedings. We thank Lajos Hajdu and Jan K. Kowalski for their efficient secretarial assistance. Special thanks go to Jan K. Kowalski, who looked through the manuscripts, made corrections, and offered valuable suggestions for improving the presentation. The staff of Walter de Gruyter & Co., especially Manfred Karbe, deserve our thanks for an excellent co-operation. We gratefully acknowledge the support of our sponsors: the Stefan Banach Cen- ter, the State Committee for Scientific Research of Poland (KBN), the Department of Defense of the Polish government, the Foundation for Polish-German Coopera- vi Preface

tion, the Max-Planck-Institut f¨ur Mathematik in Bonn, Germany, and the Stefan Batory Foundation. The organizers want to thank Don Zagier, Director of the Max-Planck-Institut, our first sponsor, for his help and friendly interest. The wonderful blackboards and some electronic equipment, purchased partially from money received from the Max-Planck-Institut, were passed on as a gift to the Mathematical Conference

Center in Be,dlewo, Poland.

September, 1998 K´alm´an Gy˝ory Henryk Iwaniec Jerzy Urbanowicz