## Theta functions with applications to Riemann surfaces |

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### Contents

Chapter | 3 |

Chapter II | 10 |

Theta indices and theta identities | 19 |

Copyright | |

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2-theta Abel's theorem abelian differentials analytic argument At(S Ax(S azygetic set base point branch points canonical homology basis Chapter character column compact Riemann surface complex congruence Corollary cycle define Definition denote derive diagonal divisor elements entries equations Farkas follows fundamental group fundamental set g X g g-vectors genus g given Hence holomorphic hyperelliptic surface implies indices integral Krazer Lemma linear linearly independent Math Max Noether meromorphic function moduli multiplier normal observe obtain odd characteristics odd thetas order theta particular period matrix poles principal set proof of Theorem prove quadratic differentials Rauch and Lebowitz reduced characteristic reduction formula references Riemann theta Riemann theta function Riemann-Roch theorem Schottky Section set of half-periods Sp(g subset surface of genus symbol symplectic syzygetic Theorem 13 Theorem 9 theta constants theta functions theta matrix tion transformation uniform products vanish identically vector Weierstrass points