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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1969 Feb;62(2):320–325. doi: 10.1073/pnas.62.2.320

THETA CONSTANTS, MODULI, AND COMPACT RIEMANN SURFACES

H M Farkas 1
PMCID: PMC277790  PMID: 16578693

Abstract

One of the classical tools for the study of moduli of compact Riemann surfaces is the Riemann theta function. Preliminary results were announced earlier1 which established relations between two kinds of theta constants on a compact Riemann surface of genus 2. In this note we generalize the results there obtained. The main theorem is as follows:

A sufficient condition for [Formula: see text] to be independent of [Formula: see text] is that [Formula: see text] for the 2g-2(2g-1 - 1) characteristics [Formula: see text] where [Formula: see text] ranges over all odd g - 1 characteristics.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Rauch H. E., Farkas H. M. Relations between two kinds of theta constants on a riemann surface. Proc Natl Acad Sci U S A. 1968 Jan;59(1):52–55. doi: 10.1073/pnas.59.1.52. [DOI] [PMC free article] [PubMed] [Google Scholar]

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