## Topics in Complex Function Theory: Abelian functions and modular functions of several variables |

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### Contents

CHAPTER | 1 |

The preparation theorem | 4 |

Regular functions | 13 |

Copyright | |

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Abelian functions abelian varieties abs CW Akad algebraic variety Amer arbitrary assume automorphic functions bounded Chapter 3 Volume coefficients columns compact condition constant coordinates corresponding defined degree denote diagonal divisor Eisenstein series Ek(W elements elliptic modular entire function equation exponent system factor system finitely fixed follows formula function field fundamental region Furthermore given Hence Hermitian implies inequalities integral intersection invertible Jacobian functions linear transformation mapping Math meromorphic function modular forms modular functions modular group modular matrix modular substitution Modulformen Modulfunktionen n-disk natural number neighborhood nondegenerate obtain period matrix Picard variety polynomial positive number power series proof of Theorem proved quadratic quotient rational functions regular function relation relatively prime respect Riemann rows satisfied Section solution space sufficiently small suitable symplectic theory theta functions unimodular uniquely determined unit Univ vanish identically variables z1 view of Theorem yields zero