Veech surfaces with non-periodic directions in the trace field (2009)
Arnoux, Pierre, Schmidt, Thomas A.
We show that each of Veech's original examples of translation surfaces with ``optimal dynamics'' whose trace field is of degree greater than two has non-periodic directions of vanishing...
Quilting natural extensions for alpha-Rosen Fractions (2009)
Kraaikamp, Cor, Schmidt, Thomas A., Smeets, Ionica
We give natural extensions for the alpha-Rosen continued fractions of Dajani et al. for a set of small alpha values by appropriately adding and deleting rectangles from the region of the natural...
Veech surfaces with non-periodic directions in the trace field (2009)
Arnoux, Pierre, Schmidt, Thomas A.
Veech's original examples of translation surfaces Vq enjoying what McMullen has dubbed "optimal dynamics" arise from appropriately gluing sides of two copies of the regular q- gon, with q Ï 3 . We...
Metric and arithmetic properties of mediant-Rosen maps (2008)
Kraaikamp, Cor, Nakada, Hitoshi, Schmidt, Thomas A.
A continued fractions based verification of the Hurwitz values for the Hecke triangle groups is given, completing a program of Lehner's. Ergodic theory shows that Diophantine approximation by mediant...
McShane's identity, using elliptic elements (2008)
Schmidt, Thomas A., Sheingorn, Mark
We introduce a new method to establish McShane's Identity, based upon the fact that elliptic elements of order two in the Fuchsian group uniformizing the quotient of a fixed once-punctured hyperbolic...
Tong's spectrum for Rosen continued fractions (2007)
Kraaikamp, Cor, Schmidt, Thomas A., Smeets, Ionica
The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best possible upper bound...
Geometry of infinitely generated Veech groups (2004)
Hubert, Pascal, Schmidt, Thomas A.
Veech groups uniformize Teichm\"uller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely...
Low height geodesics and the Markoff spectrum (2004)
Schmidt, Thomas A., Sheingorn, Mark
We classify, in terms of topology of highest arcs, low height non-simple geodesics on the modular hyperbolic punctured sphere with three elliptic fixed points of order two. Of eight possible types,...
Thesis (Ph. D.)--Saint Louis University, 2001.
Generating Elliptic Curves of Prime Order (2001)
Thomas A. Schmidt, Çetin K. Koç
Abstract. Avariation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed. We give heuristics and timing statistics in the mildly...
Generating Elliptic Curves of Prime Order (2001)
Erkay Savas Thomas, Thomas A. Schmidt, Çetin K. Koç
Avariation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed.
Closed curves and geodesics with two self-intersections on the Punctured torus (1998)
Schmidt, Thomas A., Wiles, Peter, Insel, Thomas, Dziadosz, Susan, Garity, Dennis J., Crisp, David
We classify the free homotopy classes of closed curves with minimal self intersection number two on a once punctured torus, T , up to homeomorphism. Of these, there are six primitive classes and two...
Veech Groups And Polygonal Coverings (1998)
Pascal Hubert, Thomas A. Schmidt
. We discuss branch points and their effects on Veech groups. In particular, this allows us to show that even if one polygon tiles another, the respective Veech groups are not necessarily...
Digoxin affects potassium homeostasis during exercise in patients with heart failure (1995)
Schmidt, Thomas A, Bundgaard, Henning, Olesen, Hanne L, Secher, Niels H, Kjeldsen, Keld
Objective: The aim was to evaluate whether digitalisation of heart failure patients affects extrarenal potassium handling during and following exercise, and to assess digoxin receptor occupancy in...