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Budarina, Natalia, 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: | 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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/10110 |
| 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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