Geodesic
Eichler -- Shimura relations for theta functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 152-157

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In this paper, the three-term identity of the Jacobi theta functions in two variables is interpreted as the Eichler-Shimura relation. This allows us to construct new classes of identities of this type with the help of Hecke operators. 
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     author = {V. A. Bykovskii},
     title = {Eichler -- {Shimura} relations for theta functions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {152--157},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a2/}
}
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V. A. Bykovskii. Eichler -- Shimura relations for theta functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 152-157. http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a2/