Jacobi form and distribution formulas
The authors develop the theory of distribution relations for modular units. They prove a stronger version of distribution formulas appearing in the literature (due notably to Kubert, Coates and Robert), identifying a particular root of unity appearing in the formulas. Perhaps surprisingly, the roots of unity which appear are 8th roots, whereas in the work of \textit{G. Robert} [Invent. Math. 100, 231--257 (1990; Zbl 0729.11029)] and \textit{J. Coates} [Bull. Lond. Math. Soc. 23, 321--350 (1991; Zbl 0752.11024)], it is 12th roots which appear most naturally. The proofs involve first studying the distribution relations satisfied by the Klein functions [see \textit{D. Kubert} and \textit{S. Lang}, Modular units (Grundlehren der mathematischen Wissenschaften. 244, Springer, New York-Heidelberg-Berlin) (1981; Zbl 0492.12002)], and then relating other elliptic units to the Klein functions. The main application of such results would be towards an elliptic version of Zagier's conjecture; at the moment, motivic cohomology is defined as Adams eigenspaces of rational K-groups, so that these roots of unity play no role. One might hope for an integral version of motivic cohomology; in this case, knowledge of the exact roots of unity appearing would be of great interest.
scientific article; zbMATH DE number 2136924