Number theory in function fields/ Michael Rosen.
Series: Graduate texts in mathematics ; 210Publication details: New York: Springer, c2002.Description: xii, 358 p.; 25 cmISBN:- 0387953353 (alk. paper)
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| Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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Castorina Estantes Abertas (Open Shelves) | Livros (Books) | 1 | Checked out | 2024-09-30 | 39063000596851 |
Includes bibliographical references (p. [341]-351) and index.
Preface -- 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 .
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