Periods of hyperelliptic integrals expressed in terms of θ -constants by means of Thomae formulae-Reference-Cited by-同舟云学术

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

Published:2007-06-26 Issue:1867 Volume:366 Page:1005-1024
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Enolski Victor¹,Richter Peter²

Affiliation:

1. Department of Mathematics and Statistics, Concordia University1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G 1M8

2. Institut für Theoretische Physik and Institut für Dynamische Systeme, Universität BremenPostfach 33 04 40, Bremen 28334, Germany

Abstract

Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of θ -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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2007.2059

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