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

• Autores: Natalia Budarina, Detta Dickinson, Vasili Bernik
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 149, Nº 2, 2010, págs. 193-216
• Idioma: inglés
• DOI: 10.1017/s0305004110000162
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• Resumen

  • 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.