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

Published online by Cambridge University Press:  10 May 2010

NATALIA BUDARINA
Affiliation:
Department of Mathematics, NUI Maynooth, Co Kildare, Ireland. e-mail: d.dickinson@maths.may.ie
DETTA DICKINSON
Affiliation:
Department of Mathematics, NUI Maynooth, Co Kildare, Ireland. e-mail: d.dickinson@maths.may.ie
VASILI BERNIK
Affiliation:
Department of Mathematics,Surganova 9, Minsk, Belarus.

Abstract

In this paper it is shown that if the volume sum ∑r = 1 Ψ(r) converges for a monotonic function Ψ then the set of points (x, z, w) ∈ ℝ × ℂ × ℚp which simultaneously satisfy the inequalities |P(x)| ≤ Hv1 Ψλ1(H), |P(z)| ≤ Hv2 Ψλ2(H) and |P(w)|pH−v3 Ψλ3(H) with v1 + 2v2 + v3 = n − 3 and λ1 + 2λ2 + λ3 = 1 for infinitely many integer polynomials P has measure zero.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

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