Geodesic
On the arithmetic nature of some identities of the elliptic functions theory
Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 15-34

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The article offers a new arithmetic method of proof of the classical triple, quintuple and octuple product identities of the theta functions theory. 
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V. A. Bykovskii; M. D. Monina. On the arithmetic nature of some identities of the elliptic functions theory. Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 15-34. http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a1/