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Concernant la relation de distribution satisfaite par la fonction φ associée à un réseau complexe

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Summary

For any pair of latticesL andL satisfying i)L⊂L and ii) the indexN ofL intoL is prime to 6, we construct from the usual φ-function ofL(cf. no 1) some elliptic function

$$\psi = \psi (z;L,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{L} )$$

of the variablez, with period latticeL, and divisor

$$N(0)_L - \sum\limits_{i - 1}^N {(t_i )_L } $$

over the torus ℂL, where the complex numberst i , 1≦i≦N, describe a complete set of representatives of the quotientL/L.

The set of all these functions satisfy the distribution relation (1) below.

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  1. Institut Fourier, Mathématiques, Université de Grenoble I, B.P. 74, F-38402, Saint-Martin d'Hères, France

    G. Robert

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  1. G. Robert
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Robert, G. Concernant la relation de distribution satisfaite par la fonction φ associée à un réseau complexe. Invent Math 100, 231–257 (1990). https://doi.org/10.1007/BF01231186

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