## Algebraic numbers |

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### Contents

Chapter | 1 |

Chinese remainder theorem | 8 |

Discrete valuation rings | 17 |

Copyright | |

16 other sections not shown

### Common terms and phrases

adele algebraic integers apply archimedean absolute values Artin assertion assume automorphism B/ty bounded Chapter character characteristic function coefficients complex numbers computation constant contained converges Corollary cyclotomic Dedekind ring define degree denote Dirichlet series discrete valuation ring discriminant embedded equal Euclidean exists an element factor finite extension finite number finite separable extension follows formula Fourier transform fractional ideal functional equation fundamental domain Galois group given Haar measure Hence homomorphism ideal classes idele inequality integral closure irreducible polynomial isomorphism kernel L-series lattice Lemma maximal ideal module non-zero norm number field number of elements ordp p-adic prime element prime ideal prime number principal ideal Proof Proposition Q(co quasi-character quotient field Re(s residue class residue class field restricted direct product root of unity satisfies subgroup tamely ramified Tauberian theorem theory totally ramified trivial unique unit unramified vector zeta function