Polynomials with Special Regard to Reducibility

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Cambridge University Press, Apr 27, 2000 - Mathematics
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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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Contents

Notation
8
Lacunary polynomials over an arbitrary field
92
Polynomials over an algebraically closed field
201
Polynomials over a finitely generated field
263
Polynomials over a number field
315
Polynomials over a Kroneckerian field
390
Appendices
481
Bibliography
540
Indices
555
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