Number theory in function fields/
Michael Rosen
- New York: Springer, 2002.
- xii, 358 p. ; 25 cm.
- (Graduate texts in mathematics), 210 .
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.