Jackson's formula with remainder in p-adic analysis

Abstract

Let Z p be the ring of p-adic integers. Let a and q be two units of Z p , q not a root of unity. We define V q to be the closure of the set { aq n|n = 0,1,2,…}. For continuous functions defined on V q there exists an expansion which is similar to the Mahler expansion for continuous functions on Z p . This is called Jackson's formula. We now give an expression for the remainder in Jackson's formula.