Abstract: After introducing the Lehmer Question (unanswered since 1933), we discuss lower bounds of Lehmer type for N ́eron-Tate heights on elliptic curves over the function field C(t) (before last year there were apparently no such estimates in the published literature). Then Silverman proved a result using the “Fourier Method”. I will describe an alternative method through auxiliary polynomials and an approach first used by Sieburg in his 1983 thesis (since then hardly developed in the published literature). That method is based on an analogue of Mahler’s p-adic transcendence techniques which could be crudely described as t-adic.