## Abstract

Abelian covers of CP^{1}, with fixed Galois group A, are classified, as a first step, by a discrete set of parameters. Any such cover X, of genus g ≥ 1, say, carries a finite set of A-invariant divisors of degree g−1 on X that produce nonzero theta constants on X. We show how to define a quotient involving a power of the theta constant on X that is associated with such a divisor Δ, some polynomial in the branching values, and a fixed determinant on X that does not depend on Δ, such that the quotient is constant on the moduli space of A-covers with the given discrete parameters. This generalizes the classical formula of Thomae, as well as all of its known extensions by various authors.

Original language | American English |
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Pages (from-to) | 7025-7069 |

Number of pages | 45 |

Journal | Transactions of the American Mathematical Society |

Volume | 372 |

Issue number | 10 |

DOIs | |

State | Published - 15 Nov 2019 |

### Bibliographical note

Publisher Copyright:© 2019 American Mathematical Society

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