Polynomials with Special Regard to Reducibility

Erscheinungsjahr 2014
ISBN: 978-0-521-66225-3
Verlag: Cambridge University Press

Buch, Englisch, Band 77, 568 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1013 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Schinzel, A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.