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math.NT2019
The Minkowski chain and Diophantine approximation
Nickolas Andersen, William Duke
The Hurwitz chain gives a sequence of pairs of Farey approximations to an irrational real number. Minkowski gave a criterion for a number to be algebraic by using a certain general…
math.NT2019
On a theorem of Davenport and Schmidt
Nickolas Andersen, William Duke
This work is motivated by a paper of Davenport and Schmidt, which treats the question of when Dirichlet's theorems on the rational approximation of one or of two irrationals can be…