1 Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada. vze@ma.hw.ac.uk

Periods of hyperelliptic integrals expressed in terms of theta-constants by means of Thomae formulae.

Philos Trans A Math Phys Eng Sci. 2008 Mar 28;366(1867):1005-24

Authors: Enolski V, Richter P

Abstract

Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of theta-constants. They are derived with the help of Thomae's classical formulae and Picard-Fuchs equations for complete integrals as functions of the parameters of the curves. The example of genus 2 is considered in detail.

PMID: 17594965 [PubMed]