The Ramanujan Journal

, Volume 28, Issue 1, pp 61–78

Hyperelliptic integrals and generalized arithmetic–geometric mean

Open Access
Article

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.

Keywords

Arithmetic–geometric means Hyperelliptic integrals Theta functions 

Mathematics Subject Classification (2000)

14K25 11B83 11F27 14H40 

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Copyright information

© The Author(s) 2012

Authors and Affiliations

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

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