TY  - BOOK
AU  - Rosen, Michael
TI  - Number theory in function fields
SN  - 9780387953359
U1  - 512.7 
PY  - 2002///
CY  - New York
PB  - Springer
KW  - Number theory
KW  - Algebraic Geometry
KW  - Mathematics
N1  - 1. Polynomials over finite fields --
2. Primes, Arithmetic functions, and the zeta function --
3. The reciprocity law --
4. Dirichlet L-series and primes in an arithmetic progression --
5. Algebraic function fields and global function fields --
6. Weil differentials and the canonical class --
7. Extensions of function fields, Riemann-Hurwitz, and the ABC theorem --
8. Constant field extensions --
9. Galois extensions : Hecke and Artin L-series --
10. Artin's primitive root conjecture --
11. The behavior of the class group in constant field extensions --
12. Cyclotomic function fields --
13. Drinfeld modules : an introduction --
14. S-units, S-class group, and the corresponding L-functions --
15. The Brumer-Stark conjecture --
16. The class number formulas in quadratic and cyclotomic function fields --
17. Average value theorems in function fields --
Appendix. A proof of the function field Riemann hypothesis
ER  -