\(p\)-adic measures and formal groups (Q687536)

Let \(\mathbb{Z}_ p\) (resp. \({\mathcal O}\)) be the ring of integers of \(\mathbb{Q}_ p\) (resp. of a finite extension \(K\) of \(\mathbb{Q}_ p\)). Given an \({\mathcal O}\)-valued measure on \(\mathbb{Z}_ p^ n\), the author defines an \(n\)-variable \(L\)-function whose special values at the non-positive integers coincide with the moments of this measure. Such a measure corresponds to an \(n\)-dimensional formal group over \(K\) of the type considered in the author's joint papers with \textit{J. Stopple} [J. Number Theory 41, 283--294, 295--302 (1992; Zbl 0762.11047, Zbl 0762.11046)].