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This paper shows how some techniques used for the meromorphic functions of one variable can be used for the explicit construction of a solution to the Mittag-Leffler problem for Dolbeault classes of tipe $(0,n-1)$ with singularities in a discrete set of ${𝐂}^{𝐧}$ and $T^n$ (a $n$-dimensional complex torus). A generalisation is given for the Weierstrass $\zeta$ and the Legendre relations.

In this paper some series of Weierstrass’ $𝒫$ (and its derivatives) type are constructed by means of the Bochner-Martinelli kernels. The Dolbeault cohomology classes of such series generate $H^{0,n-1}(T^n\mathrm{—}\{0\})$, where $T^n$ stands for the $n$-dimensional complex torus.

This paper shows how some techniques used for the meromorphic functions of one variable can be used for the explicit construction of a solution to the Mittag-Leffler problem for Dolbeault classes of tipe $(0,n-1)$ with singularities in a discrete set of ${𝐂}^{𝐧}$ and $T^n$ (a $n$-dimensional complex torus). A generalisation is given for the Weierstrass $\zeta$ and the Legendre relations.

We consider the representation of a Siegel half-plane associated with the polarized torus of dim 2m obtained by the periods of the holomorphic 2m-forms. In particular, for m=1 we obtain the geometric significance of the isomorphism between a Siegel half-plane of dimension three and the domain of type IV of the same dimension.