Polynomials with special regard to reducibility / A. Schinzel.

Format:

Book

Author/Creator:

Schinzel, Andrzej, author.

Series:

Encyclopedia of mathematics and its applications ; v. 77.

Encyclopedia of mathematics and its applications ; volume 77

Language:

English

Subjects (All):

Polynomials.

Physical Description:

1 online resource (x, 558 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2000.

Language Note:

English

Summary:

This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Results valid only over finite fields, local fields or the rational field are not covered here, but several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields are included. Some of these results are based on recent work of E. Bombieri and U. Zannier (presented here by Zannier in an appendix). The book also treats other subjects like Ritt's theory of composition of polynomials, and properties of the Mahler measure, and it concludes with a bibliography of over 300 items. This unique work will be a necessary resource for all number theorists and researchers in related fields.

Contents:

1. Arbitrary polynomials over an arbitrary field

2. Lacunary polynomials over an arbitrary field

3. Polynomials over an algebraically closed field

4. Polynomials over a finitely generated field

5. Polynomials over a number field

6. Polynomials over a Kroneckerian field

App. A. Algebraic functions of one variable

App. B. Elimination theory

App. C. Permutation groups and abstract groups

App. D. Diophantine equations

App. E. Matrices and lattices

App. F. Finite fields and congruences

App. G. Analysis

App. I. Inequalities

App. J. Distribution of primes

App. K. Convexity

App. Proof of Conjecture 1 / Umberto Zannier.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 540-554) and index.

ISBN:

1-107-11845-X

1-280-42092-8

9786610420926

0-511-17245-1

0-511-15123-3

0-511-31053-6

0-511-54291-7

0-511-04894-7

OCLC:

437072440