Poincaré's work on the reduction of Abelian integrals contains implicitly an algorithm for the expression of a theta function as a sum of products of theta functions of fewer variables in the presence of reduction. The aim of this paper is to give explicit formulations and reasonably complete proofs of Poincaré's results.
@article{urn:eudml:doc:41164,
title = {A footnote to the Poincar\'e complete reducibility theorem.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {111-129},
zbl = {0780.30031},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41164}
}
Martens, Henrik H. A footnote to the Poincaré complete reducibility theorem.. Publicacions Matemàtiques, Tome 36 (1992) pp. 111-129. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41164/