Effective approximation to complex algebraic numbers by quadratic numbers
Prajeet Bajpai, Yann Bugeaud
TL;DR
This paper improves the bounds on how well complex non-real algebraic numbers can be approximated by quadratic algebraic numbers, refining a classical inequality.
Contribution
It provides an effective enhancement of Liouville's inequality specifically for complex algebraic numbers approximated by quadratic algebraic numbers.
Findings
Improved approximation bounds for complex algebraic numbers
Effective version of Liouville inequality for quadratic approximations
Enhanced understanding of approximation quality in complex algebraic number theory
Abstract
We establish an effective improvement on the Liouville inequality for approximation to complex non-real algebraic numbers by quadratic complex algebraic numbers.
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Taxonomy
TopicsIterative Methods for Nonlinear Equations · Numerical Methods and Algorithms · Approximation Theory and Sequence Spaces