\(p\)-adic Banach modules of arithmetical modular forms and triple products of Coleman's families (Q959028)

The author describes a four variable \(p\)-adic \(L\)-function attached to Garrett's triple product of three Coleman's families of cusp eigenforms. The article extends a previous result of the author [Invent. Math. 154, No. 3, 551--615 (2003; Zbl 1065.11025)], where a two variable \(p\)-adic \(L\)-function attached to one Coleman's family was constructed. Details of computations and proofs are contained in a joint article with \textit{S. Böcherer} [\(p\)-adic interpolation for triple \(L\)-functions: analytic aspects, in: Automorphic forms and \(L\)-functions II. Local aspects. Isr. Math. Conf. Proc., Contemp. Math. 489, 1--39 (2009; Zbl 1275.11083)].