The cubic simplectic theta function
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 148-158

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It is proved that the cubic symplectic theta function is invariant with respect to the group $\operatorname{Sp}(4,\mathbb Z)$.
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     author = {N. V. Proskurin},
     title = {The cubic simplectic theta function},
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N. V. Proskurin. The cubic simplectic theta function. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 148-158. http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a10/