Formes de Jacobi et formules de distribution

The main theorem proved in this paper consists of a multiplicative distribution formula for the Jacobi forms in two variables associated to Klein forms. This gives stronger versions of distribution formulae appearing in the literature. Indeed, as a first consequence of the main theorem, we deduce an optional proof of the distribution formula true for any elliptic function first found by Kubert and as a second consequence, we prove an ameliorated distribution formula for a certain zeta function previously treated by Coates, Kubert and Robert. Moreover, our main theorem provides the exact root of unity appearing in the distribution formula of Jarvis and Wildeshaus, a fact which could be useful in the K-theory of elliptic curves or more precisely, in the investigation of the elliptic analogue of Zagier's conjecture linking regulators and polylogarithms.