16 citations · 16 across the 8 of their papers we have counts for
12 papers
Non-convex geometry of numbers and continued fractions
Nickolas Andersen, William Duke, Zach Hacking +1
In recent work, the first two authors constructed a generalized continued fraction called the -continued fraction, characterized by the property that its convergents (a subseque…
Asymptotic distribution of traces of singular moduli
Nickolas Andersen, William Duke
We determine the asymptotic behavior of twisted traces of singular moduli with a power-saving error term in both the discriminant and the order of the pole at . Using this…
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…
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…
Markov spectra for modular billiards
Nickolas Andersen, William Duke
We introduce some analogues of the Markov spectrum defined in terms of modular billiards and consider the problem of characterizing that part of the spectrum below the lowest limit…
Modular invariants for real quadratic fields and Kloosterman sums
Nickolas Andersen, William Duke
We investigate the asymptotic distribution of integrals of the -function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asympt…