, Volume 28, Issue 1, pp 61-78,
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Date: 01 Mar 2012

Hyperelliptic integrals and generalized arithmetic–geometric mean

Abstract

We show how certain determinants of hyperelliptic periods can be computed using a generalized arithmetic-geometric mean iteration, whose initialisation parameters depend only on the position of the ramification points. Special attention is paid to the explicit form of this dependence and the signs occurring in the real domain.

Part of the work was done with the support of the SFB/TR 45 during a stay of the first author at the Johannes Gutenberg University in Mainz.