## Analytic Functions of Several Complex Variables: Lectures Delivered at the Institute for Advanced Study, 1948-1949 |

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### Contents

2 The i eierstruss Preparation Theorem | 3 |

3 The Analogue of Euclids Lemma | 5 |

4 The Quotient Field of the Ring of Power Series | 8 |

47 other sections not shown

### Common terms and phrases

2n by 2n 2n matrix 2n strongly independent Abelian functions absolute value algebraic function field algebraic surface algebraicly independent analytic mappings analytically independent automorphic forms automorphic functions bounded domain choose closed subset coefficients compact analytic manifold complex dimension complex numbers complex variables condition consider constant coordinate coprime direct continuations discontinuous group discrete subgroup divisor entire function equation equivalence class exists finitely function f function regular fundamental region Gaussian integers group of analytic Hence Henoe Hermitian homeomorphic identically zero integral Jacobian functions lemma limit point linear mapping linear transformations meromorphic functions meromorphio modular forms modular function modular group modulo n-circle neighborhood non-degenerate function non-singular period matrix point set polyhedral domain positive integer positive number power series proof proved quotient replaced right cosets roup satisfy space strongly independent periods Suppose Theorem 12 theta functions thut unimodular unit unit-circle upper half-plane v/here