Far Eastern Mathematical Journal

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Eichler-Shimura relations for theta functions


Bykovskii V.A.

2017, issue 2, Đ. 152-157


Abstract
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.

Keywords:
Jacobi theta functions, Eichler-Shimura relations, Hecke operators, Eichler-Shimura moduli

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References

[1] C.G.J. Jacobi, Gesammelte Werke, v. 1, Berlin, 1881.
[2] H.M. Weber, Lehrbuch der Algebra, v. 3, Braunschweig, 1908.
[3] A.E. Polishchuk, Abelevy mnogoobraziia, teta-funktsii i preobrazovanie Fur'e, MTsNMO, M., 2010.
[4] Iu.I. Manin, ôParabolicheskie tochki i dzeta-funktsii moduliarnykh krivykhö, Izv. AN SSSR, seriia matem., 36, (1972), 19ľ66.
[5] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press., NJ, 1971.

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