Projects per year
Abstract
Simultaneous Diophantine approximation is concerned with the approximation of a point x∈ R^{d} by points r∈ Q^{d}, with a view towards jointly minimizing the quantities ‖ x r‖ and H(r). Here H(r) is the socalled “standard height” of the rational point r. In this paper the authors ask: What changes if we replace the standard height function by a different one? As it turns out, this change leads to dramatic differences from the classical theory and requires the development of new methods. We discuss three examples of nonstandard height functions, computing their exponents of irrationality as well as giving more precise results. A list of open questions is also given.
Original language  English 

Pages (fromto)  577618 
Number of pages  42 
Journal  Monatshefte fur Mathematik 
Volume  182 
Issue number  3 
Early online date  18 Oct 2016 
DOIs  
Publication status  Published  1 Mar 2017 
Bibliographical note
© The Author(s) 2016.Keywords
 Continued fractions
 Diophantine approximation
 Dirichlet’s theorem
 Hardy Lfunctions
 Height functions
Projects
 1 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research