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Number theory in function fields/ Michael Rosen

By: Rosen, MichaelMaterial type: Text

TextSeries: (Graduate texts in mathematics) ; 210Publication details: New York: Springer, 2002Description: xii, 358 p. ; 25 cmISBN: 9780387953359Subject(s): Number theory | Algebraic Geometry | MathematicsDDC classification: 512.7

Contents:

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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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	512.7 ROS/N (Browse shelf(Opens below))	Checked out	05/06/2021	P25344

Total holds: 0

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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