An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3
Lehavi, D. ; Ritzenthaler, C.
Experiment. Math., Tome 16 (2007) no. 1, p. 421-440 / Harvested from Project Euclid
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The arithmetic--geometric mean algorithm for calculating elliptic integrals of the first type was introduced by Gauss. The analogous algorithm for abelian integrals of genus $2$ was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for abelian integrals of genus 3.
Publié le : 2007-05-15
Classification:  Prym varieties,  arithmetic geometric mean,  14H40,  14H45,  14Q05 
@article{1204836513,
     author = {Lehavi, D. and Ritzenthaler, C.},
     title = {An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3},
     journal = {Experiment. Math.},
     volume = {16},
     number = {1},
     year = {2007},
     pages = { 421-440},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204836513}
}

Lehavi, D.; Ritzenthaler, C. An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3. Experiment. Math., Tome 16 (2007) no. 1, pp.  421-440. http://gdmltest.u-ga.fr/item/1204836513/