Budarina, Natalia and Dickinson, Detta and Bernik, Vasili (2010) Simultaneous Diophantine approximation in the real, complex and p–adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 149 (2). pp. 193-216. ISSN 1469-8064

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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)| ≤ H−v1 Ψλ1(H), |P(z)| ≤ H−v2 Ψλ2(H) and |P(w)|p ≤ H−v3 Ψλ3(H) with v1 + 2v2 + v3 = n − 3 and λ1 + 2λ2 + λ3 = 1 for infinitely many integer polynomials P has measure zero.

Item Type:	Article
Additional Information:	Cite as: BUDARINA, N., DICKINSON, D., & BERNIK, V. (2010). Simultaneous Diophantine approximation in the real, complex and p–adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 149(2), 193-216. doi:10.1017/S0305004110000162
Keywords:	Simultaneous Diophantine approximation; real, complex and p–adic fields;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	10110
Identification Number:	https://doi.org/10.1017/S0305004110000162
Depositing User:	Dr. Detta Dickinson
Date Deposited:	16 Oct 2018 16:38
Journal or Publication Title:	Mathematical Proceedings of the Cambridge Philosophical Society
Publisher:	Cambridge University Press
Refereed:	Yes
URI:	https://www.cambridge.org
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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