## Elliptic Functions and Rings of Integers |

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### Contents

The KroneckerWeber Theorem | 1 |

CLASSFIELD THEORY | 9 |

Dirichlet density | 25 |

Copyright | |

1 other sections not shown

### Common terms and phrases

6-division point abelian extension algebraic integer apply Artin map C-lattice called Chapter character clear coefficients complex complex multiplication conclude conductor consequence consider constant contains coprime Corollary cusps deduce define Definition denote describe discriminant dividing division divisor element elliptic curve elliptic functions equality establish exists fact finite follows formal group formula Fueter functions Furthermore Galois action given hand Hence holomorphic immediate induces integer isomorphism Lemma let a denote maximal modular function module Moreover natural non-zero notation obtain Ox-ideal particular poles polynomial positive integer prime prime ideal primitive Proof Proposition prove q-expansion ramified recall Remark representatives resp result rings of integers root of unity shown side split structure subgroup suffice to show suppose Theorem unique unit VIII Weierstrass write zero