FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Eichler-Shimura relations for theta functions |
Bykovskii V.A. |
2017, issue 2, P. 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, “Parabolicheskie tochki i dzeta-funktsii moduliarnykh krivykh”, Izv. AN SSSR, seriia matem., 36, (1972), 19–66. [5] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press., NJ, 1971. |