## Analytic Functions of Several Complex Variables |

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### Contents

3 The Analogue of Euclids Lemma | 6 |

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

7 Definition of a eromorphic Function | 12 |

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### Common terms and phrases

2n by 2n 2n independent 2n matrix 2n strongly independent 2TTi Abelian function algebraic function field analytic manifold analytic mappings assume bilinear form bounded domain coefficients common divisor compact analytic manifold complex dimension complex numbers complex variables consider constant coprime direct continuations direct product discontinuous group entire function equation equivalence classes exists f and g field of Abelian finite number function f function regular funotion Gaussian integers Hence henoe Hermitian identically zero integral elements Jacobian functions lemma linear mapping linear transformations meromorphic functions meromorphio modular function modulo n-rowed column vectors neighborhood non-degenerate function non-degenerate type non-negative non-singular non-zero absolute value period matrix polynomial positive integer power series Problem prove quotient regular function replaced roup skew-symmetric solvable space strongly independent periods subgroup suoh Suppose symmetric Theorem 12 theta functions thut topological group unimodular matrix unique unit upper half-plane