Hyperelliptic integrals and generalized arithmetic–geometric mean
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- 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.