Goss D. Basic Structures of Function Field Arithmetic

Berlin: Springer, 1996. — 219 p.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.Additive Polynomials
Review of Non-Archimedean Analysis
The Carlitz Module
Drinfeld Modules
T-modules
Shtukas
Sign Normalized Rank 1 Drinfeld Modules
L-series
Γ-functions
Additional Topics