The Ramanujan Journal

, Volume 28, Issue 1, pp 61–78

Hyperelliptic integrals and generalized arithmetic–geometric mean

Authors

    • Delft University of Technology
  • Duco van Straten
    • Institut für MathematikJohannes Gutenberg University
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

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

Copyright information

© The Author(s) 2012