Basic Structures of Function Field Arithmetic [Paperback]

From the reviews: The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field. MR 97i:11062From the reviews: The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field. MR 97i:110621. Additive Polynomials.- 1.1. Basic Properties.- 1.2. Classification of Additive Polynomials.- 1.3. The Moore Determinant.- 1.4. The Relationship Between k[x] and k{?}.- 1.5. The p-resultant.- 1.6. The Left and Right Division Algorithms.- 1.7. The ?-adjoint of an Additive Polynomial.- 1.8. Dividing A1 by Finite Additive Groups.- 1.9. Analogs in Differential Equations/Algebra.- 1.10. Divisibl3‹