Resumen de Simultaneous Diophantine approximation in the real, complex and p�adic fields

Natalia Budarina, Detta Dickinson, Vasili Bernik

• In this paper it is shown that if the volume sum ?r = 18 ?(r) converges for a monotonic function ? then the set of points (x, z, w) ? R × C × Qp which simultaneously satisfy the inequalities |P(x)| = H-v1 ??1(H), |P(z)| = H-v2 ??2(H) and |P(w)|p = H-v3 ??3(H) with v1 + 2v2 + v3 = n - 3 and ?1 + 2?2 + ?3 = 1 for infinitely many integer polynomials P has measure zero.