Minoration effective de la distancep-adique entre puissances de nombres algébriques Original Research Article

We use the new tool of interpolation determinants to get precise lower bounds for thep-adic distance between two integral powers of algebraic numbers. This work is thep-adic analogue of the two papers (M. Laurent,Acta Arith.66, No. 2 (1994), 181–199; M. Laurentet al.,J. Number Theory55(1995), 285–321) on which it is based, although several new specificp-adic ideas are introduced here.