Polynomials
This comprehensive book covers both long-standing results in the theory of polynomials and recent developments which have until now only been available in the research literature. After initial chapters on the location and separation of roots and on irred
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Victor V. Prasolov
Polynomials Translated from the Russian by Dimitry Leites
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Victor V. Prasolov Independent University of Moscow Department Mathematics Bolshoy Vlasievskij per.11 119002 Moscow, Russia e-mail: [email protected]
Dimitry Leites (Translator) Stockholm University Department of Mathematics 106 91 Stockholm, Sweden e-mail: [email protected]
Originally published by MCCME Moscow Center for Continuous Math. Education in 2001 (Second Edition)
Mathematics Subject Classification (2000): 12-XX, 12E05
Library of Congress Control Number: 2009935697
ISSN 1431-1550 ISBN 978-3-540-40714-0 (hardcover) ISBN 978-3-642-03979-9 (softcover) DOI 10.1007/978-3-642-03980-5
e-ISBN 978-3-642-03980-5
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2004, First softcover printing 2010 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset by the translator. Edited and reformatted by LE-TeX, Leipzig, using a Springer LATEX macro package. Cover design: deblik, Berlin Printed on acid-free paper
Preface
The theory of polynomials constitutes an essential part of university courses of algebra and calculus. Nevertheless, there are very few books entirely devoted to this theory.1 Though, after the first Russian edition of this book was printed, there appeared several books2 devoted to particular aspects of the polynomial theory, they have almost no intersection with this book. 1
2
The following classical references (not translated into Russian and therefore not mentioned in the Russian editions of this book) are rare exceptions: Barbeau E. J., Polynomials. Corrected reprint of the 1989 original. Problem Books in Mathematics. Springer-Verlag, New York, 1995. xxii+455 pp.; Borwein P., Erd´elyi T., Polynomials and polynomial inequalities. Graduate Texts in Mathematics, 161. Springer-Verlag, New York, 1995. x+480 pp.; Obreschkoff N., Verteilung und Berechnung der Nullstellen reeller Polynome. (German) VEB Deutscher Verlag der Wissenschaften, Berlin 1963. viii+298 pp. For example, some recent ones: Macdonald I. G., Affine Hecke algebras and orthogonal polynomials. Cambridge Tracts in Mathematics, 157. Cambridge University Press, Cambridge, 2003. x+175 pp.; Philli
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