Formes de Jacobi et formules de distribution

✍ Scribed by Abdelmejid Bayad; Jesús Gómez Ayala

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 293 KB
• Volume: 109
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.06.011

✦ Synopsis

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.