Number Theory in Function Fields
Springer-Verlag New York Inc.
978-0-387-95335-9 (ISBN)
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.- Author Index.
Reihe/Serie | Graduate Texts in Mathematics ; 210 |
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Zusatzinfo | XI, 358 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 156 x 234 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Naturwissenschaften ► Physik / Astronomie | |
ISBN-10 | 0-387-95335-3 / 0387953353 |
ISBN-13 | 978-0-387-95335-9 / 9780387953359 |
Zustand | Neuware |
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