Polynomials with special regard to reducibility / A. Schinzel.

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

Print version record.

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.

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.

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