Eichler – Shimura relations for theta functions

V. A. Bykovskii

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

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.

Key words: Jacobi theta functions, Eichler – Shimura relations, Hecke operators, Eichler – Shimura moduli.

UDC: 511.384

MSC: 11F67

Received: 24.10.2017

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