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

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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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/

[1] C. G. J. Jacobi, Gesammelte Werke, v. 1, Berlin, 1881

[2] H. M. Weber, Lehrbuch der Algebra, v. 3, Braunschweig, 1908 | MR

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

[4] Yu. I. Manin, “Parabolicheskie tochki i dzeta-funktsii modulyarnykh krivykh”, Izv. AN SSSR, seriya matem., 36 (1972), 19–66 | Zbl

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