10 citations · 22 across the 12 of their papers we have counts for
12 papers
A note on right-angled, ideal hyperbolic polyhedra
Ian Whitehead
We prove a necessary and sufficient condition for an abstract polyhedron to be realized as a right-angled, ideal polyhedron in hyperbolic space.
Arithmetic Polyhedra
Daniel Allcock, Pat Devlin, Anna Felikson +2
The Koebe-Andreev-Thurston theorem assigns a 3-dimensional hyperbolic reflection group to each combinatorial polyhedron. A natural question is: which of them are arithmetic? In 201…
The Local-Global Conjecture is False for Generalized Circle Packings
Hanqi Shi, Wenyuan Shi, Ian Whitehead +2
Haag, Kertzer, Rickards, and Stange disprove the Local-Global Conjecture for Apollonian circle packings. We extend their disproof to four more types of integral circle packing: the…
Functional equations of axiomatic multiple Dirichlet series, Weyl groupoids, and quantum algebra
Will Sawin, Ian Whitehead
We prove functional equations for multiple Dirichlet series defined by a collection of five geometric axioms. We find functional equations of two types: one modeled on the function…
Circle Packings from Tilings of the Plane
Philip Rehwinkel, Ian Whitehead, David Yang +1
We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The existence and uniqueness of these pa…
Domains of Convergence for Polyhedral Packings
Nooria Ahmed, William Ball, Ellis Buckminster +6
Polyhedral circle packings are generalizations of the Apollonian packing. We develop the theory of the Apollonian group, Descartes quadratic form, and related objects for all polyh…
Apollonian Packings and Kac-Moody Root Systems
Ian Whitehead
We study Apollonian circle packings in relation to a certain rank 4 indefinite Kac-Moody root system . We introduce the generating function of a packing, an expo…
Correction factors for Kac-Moody groups and -deformed root multiplicities
Dinakar Muthiah, Anna Puskás, Ian Whitehead
We study a correction factor for Kac-Moody root systems which arises in the theory of -adic Kac-Moody groups. In affine type, this factor is known, and its explicit computation…
On the third moment of II: the number field case
Adrian Diaconu, Ian Whitehead
We establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet -functions at the central value. In addition to the main term, which is known, we prove…
Affine Weyl Group Multiple Dirichlet Series: Type
Ian Whitehead
We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system , generalizing the theory of multiple D…
Multiple Dirichlet Series for Affine Weyl Groups
Ian Whitehead
Let be the Weyl group of a simply-laced affine Kac-Moody Lie group, excepting for even. We construct a multiple Dirichlet series , mer…
A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials
S. Ali Altug, Sandro Bettin, Ian Petrow +2
We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict…