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Generalizations of Thomae's Formula for Zn Curves

Part of the Developments in Mathematics Book Series (volume 21)

DOI: 10.1007/978-1-4419-7847-9

ISBN: 978-1-4419-7846-2

Publisher: Springer New York - Springer Journals

Nov 1, 2010

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Chapter 1Riemann Surfaces

Farkas, Hershel M.; Zemel, Shaul

Pages: 1 –30

[In this chapter we gather the information one needs to know about the general theory of Riemann surfaces and theta functions. A good reference for this material is [FK].]
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Chapter 2Zn Curves

Farkas, Hershel M.; Zemel, Shaul

Pages: 31 –74

[A Zncurve is a compact Riemann surface which is associated with the algebraic equation]
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Chapter 3Examples of Thomae Formulae

Farkas, Hershel M.; Zemel, Shaul

Pages: 75 –141

[In this chapter we present some examples of Thomae formulae for the singular and nonsingular cases. These examples are intended to help the reader assimilate the general cases.]
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Chapter 4Thomae Formulae for Nonsingular Zn Curves

Farkas, Hershel M.; Zemel, Shaul

Pages: 143 –182

[In this chapter we shall present a proof of the Thomae formula for the general non singular Zncurve associated to the equation.]
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Chapter 5Thomae Formulae for Singular Zn Curves

Farkas, Hershel M.; Zemel, Shaul

Pages: 183 –232

[In this chapter we shall present a proof of the Thomae formula for the singular Zn curve associated to the equation]
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Chapter 6Some More Singular Zn Curves

Farkas, Hershel M.; Zemel, Shaul

Pages: 233 –288

[In this chapter we treat two other cases of families of singular curves and give a few examples. Contrary to the examples in Chapter 3, which were presented to demonstrate special cases of general families, here we have no general theory and we treat these cases separately.]

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