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题名/责任者:

Number theory in function fields / Michael Rosen.

出版发行项:

[北京 : 世界图书出版公司,] 2011.

ISBN:

9787510037580

载体形态项:

xii, 358 p. ; 25 cm.

变异题名:

函数域中的数论

丛编说明:

Graduate texts in mathematics ; 210

个人责任者:

Rosen, Michael I. (Michael Ira), 1938-

论题主题:

Number theory.

论题主题:

Finite fields (Algebra)

中图法分类号:

O156

一般附注:

Cover title.

书目附注:

Includes bibliographical references (p. [341]-351) and indexes.

内容附注:

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.

原版附注:

Reprint. Originally published: New York : Springer,c2002. 0387953353.

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