Small totally p-adic algebraic numbers.

The purpose of this note is to give a short and elementary proof of the fact that the absolute logarithmic Weil-height is bounded from below by a positive constant for all totally p -adic numbers which are neither zero nor a root of unity. The proof is based on an idea of C. Petsche and gives the best known lower bounds in this setting. These bounds differ from the truth by a term of less than log (3) / p. [ABSTRACT FROM AUTHOR]