The Ramanujan Journal

, Volume 28, Issue 1, pp 61–78

Hyperelliptic integrals and generalized arithmetic–geometric mean

Open AccessArticle

DOI: 10.1007/s11139-011-9353-7

Cite this article as:
Spandaw, J. & van Straten, D. Ramanujan J (2012) 28: 61. doi:10.1007/s11139-011-9353-7


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.


Arithmetic–geometric meansHyperelliptic integralsTheta functions

Mathematics Subject Classification (2000)

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© The Author(s) 2012

Authors and Affiliations

  1. 1.Delft University of TechnologyCD DelftThe Netherlands
  2. 2.Institut für MathematikJohannes Gutenberg UniversityMainzGermany