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Elliptic modules

V. G. Drinfeld


Abstract: The notion of elliptic module is introduced, generalizing the concept of an elliptic curve, and an analog of the theory of elliptic and modular curves is constructed. Here the role of the group $GL(2,Q)$ is played by $GL(2,k)$, where $k$ is a function field. A theorem on the coincidence of $L$-functions of modular curves and Jacquet–Langlands $L$-functions corresponding to $k$ is proved.
Bibliography: 14 titles.

UDC: 519.49

MSC: Primary 10D25, 12A65; Secondary 14K22

Received: 17.12.1973

 English version: Mathematics of the USSR-Sbornik, 1974, 23:4, 561–592

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