Inventiones mathematicae

, Volume 100, Issue 1, pp 231–257

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


  • G. Robert
    • Institut Fourier, MathématiquesUniversité de Grenoble I

DOI: 10.1007/BF01231186

Cite this article as:
Robert, G. Invent Math (1990) 100: 231. doi:10.1007/BF01231186


For any pair of latticesL andL satisfying i)LL 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 numbersti, 1≦iN, describe a complete set of representatives of the quotientL/L.

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

Copyright information

© Springer-Verlag 1990