Jacobi forms and \(p\)-adic Weber formula. (Formes de Jacobi et formule de Weber \(p\)-adique.) (French) Zbl 1059.11036

From the text: The author continues his previous work with G. Robert [C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 5, 455–460 (1997; Zbl 0885.11035)] and constructs a \(p\)-adic analogue of the meromorphic complex Jacobi form \(D_L(z,\phi) (L\) a complex lattice, \(z,\phi\in\mathbb C)\). As this function can be expressed as a quotient of suitable Jacobi theta functions and Roquette’s theory of elliptic functions over local fields, the author shows that it satisfies a simple additive distribution and an inversion relation. As a consequence of this result he proves a \(p\)-adic analog of a generalized complex Weber’s formula.


11F50 Jacobi forms
11G07 Elliptic curves over local fields
11F85 \(p\)-adic theory, local fields


Zbl 0885.11035
Full Text: DOI Numdam EuDML EMIS


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