## Introduction to the Theory of Algebraic Numbers and FuctionsIntroduction to the Theory of Algebraic Numbers and Fuctions |

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### Contents

1 | |

5 | |

The Theta Function | 32 |

Chapter II Ideals and Divisors | 53 |

Topics from the Theory of Algebraic Number Fields | 98 |

Chapter III Algebraic Functions and Differentials | 110 |

Chapter IV Algebraic Functions over the Complex Number Field | 185 |

Chapter V Correspondences between Fields of Algebraic Functions | 233 |

Author Index | 321 |

322 | |

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### Common terms and phrases

algebraic function algebraic number algebraically closed arbitrary assertion assume assumption automorphisms basis canonical class coefficients congruence contains cusp forms decomposes defined degree denominator denote dimension divisible divisor classes exact constant field exists factor finite extension finite number formula Fourier function field Galois genus holds homomorphism implies integral divisor integral domain invariant isomorphic KK'ſ ko(x last section lemma linear divisor linearly independent local ring mapping Math matrix modular forms modular functions module multiplication norm number field o-ideal o-module power series prime correspondence prime decomposition prime divisors prime element prime ideal principal divisor principal ideal domain principal order principal part system Proof proved quadratic quotient ramification rational function rational integers residue class residue class field respect Riemann surface Riemann–Roch theorem ring satisfies separable extension shows subfield subgroup variable vectors yields zeros