Polynomials with Special Regard to Reducibility: 77 (Encyclopedia of Mathematics and its Applications, Series Number 77)
Cambridge University Press, 4/27/2000
EAN 9780521662253, ISBN10: 0521662257
Hardcover, 570 pages, 23.4 x 15.5 x 3.3 cm
Language: English
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.
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.