Polynomials with Special Regard to Reducibility [Hardcover]

This book covers most of the known results on reducibility of polynomials.This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Included also are results 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. This unique work will be a necessary resource for all number theorists and researchers in related fields.This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Included also are results 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. This unique work will be a necessary resource for all number theorists and researchers in related fields.This treatise covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields, and finitely generated fields. The author includes several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields. Some of these results are based on the recent work of E. Bombieri and U. Zannier, presented here by Zannier in an appendix. The book also treats other subjects such as Ritt's theory of composition of polynomials, and properties of the Mahler measure and concludes with a bibliography of over 300 items.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; Appendices; Bibliography.lN