Non-archimedean Mellin transform and \(p\)-adic \(L\)-functions (Q1388204)

In this survey article, the author describes some of the recent constructions of \(p\)-adic \(L\)-functions attached to arithmetically defined \(L\)-functions: the non-archimedean convolutions of Hilbert modular forms (section 5), \(p\)-adic families of motives and their \(L\)-functions (sections 6-8).