Geodesic
Eichler – Shimura relations for theta functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 152-157 
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/
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     author = {V. A. Bykovskii},
     title = {Eichler {\textendash} {Shimura} relations for theta functions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[3] A. E. Polischuk, Abelevy mnogoobraziya, teta-funktsii i preobrazovanie Fure, MTsNMO, M., 2010 | MR

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[5] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press., NJ, 1971 | MR | Zbl