19 papers
Lattice polytopes, Hecke operators, and the Ehrhart polynomial
Paul E. Gunnells, Fernando Rodriguez Villegas
Let P be a simple lattice polytope. We define an action of the Hecke operators on E (P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E (P). We als…
A characterization of Dynkin elements
Paul E. Gunnells, Eric Sommers
We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a Dynkin element is the unique point of minimal length in its N-region.…
Geometry of the tetrahedron space
Eric Babson, Paul E. Gunnells, Richard Scott
Let X^{circ} be the space of all labeled tetrahedra in P^{3}. In [BGS] we constructed a smooth symmetric compactification X-tilde of X^{circ}. In this article we show that the comp…
Units, polyhedra, and a conjecture of Satake
Paul E. Gunnells, Jacob Sturm
Let $F/\QQ $ be a totally real number field of degree . We explicitly evaluate a certain sum of rational functions over a infinite fan of -rational polyhedral cones in terms…
Toric modular forms of higher weight
Lev A. Borisov, Paul E. Gunnells
In two previous papers we used the geometry of complete polyhedral fans to construct a subring $\TTT (l)$ of the modular forms on , and showed that for weight two the cu…
Elliptic functions and equations of modular curves
Lev Borisov, Paul Gunnells, Sorin Popescu
Let be a prime. We show that the space of weight one Eisenstein series defines an embedding into $\PP^{(p-3)/2}$ of the modular curve for the congruence group $Γ_…