51 citations · 61 across the 13 of their papers we have counts for
17 papers
Minimal Mahler Measure in Quartic Galois Number Fields
Bishnu Paudel, Kathleen Petersen, Haiyang Wang
We explore the dependence of the minimal integral Mahler measure of Galois quartic fields on the discriminant of the field. We obtain density results which are conditional on the A…
Geometric structures and representations of knot groups from knot diagrams
Kathleen L. Petersen, Anastasiia Tsvietkova
We describe a new method of producing equations for the canonical component of representation variety of a knot group into . Unlike known methods, this one does…
Small representations of Seifert fiber space groups
Neil R Hoffman, Kathleen L Petersen
Let be a Seifert fiber space with non-abelian fundamental group and admitting a triangulation with tetrahedra. We show that there is a non-abelian $\text{PSL}(2, \mathbb{F}…
Partitions Associated to Class Groups of Imaginary Quadratic Number Fields
Kathleen Petersen, James Sellers
We investigate properties of attainable partitions of integers, where a partition of is attainable if . Conjecturally, under an ex…
Minimal Mahler Measure in Cubic Number Fields
Lydia Eldredge, Kathleen Petersen
The minimal integral Mahler measure of a number field , , is the minimal Mahler measure of a non-torsion primitive element of . Upper and lower…
Symmetries and Detection of Surfaces by the Character Variety
Jay Leach, Kathleen Petersen
We extend Culler and Shalen's construction of detecting essential surfaces in 3-manifolds to 3-orbifolds. We do so in the setting of the character varie…
Lower Bounds for Heights in Relative Galois Extensions
Shabnam Akhtari, Kevser Aktaş, Kirsti Biggs +3
The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our fir…
Missing class groups and class number statistics for imaginary quadratic fields
Samuel Holmin, Nathan Jones, Pär Kurlberg +2
The number F(h) of imaginary quadratic fields with a given class number h is of classical interest: Gauss' class number problem asks for a determination of those fields counted by…
Character varieties of double twist links
Kathleen L. Petersen, Anh T. Tran
We compute both natural and smooth models for the character varieties of the two component double twist links, an infinite family of two-bridge links indexed as $…
Gonality and genus of canonical components of character varieties
Kathleen L. Petersen, Alan W. Reid
Let M be a two cusped hyperbolic 3-manifold and let M(r) be the result of r Dehn filling of a fixed cusp of M. We study canonical components of the SL(2,C) character varieties of M…
Equidistribution of Elements of Norm 1 in Cyclic Extensions
Kathleen L. Petersen, Christopher D. Sinclair
Upon quotienting by units, the elements of norm 1 in a number field form a countable subset of a torus of dimension where and are the numbers of rea…
Character varieties of once-punctured torus bundles with tunnel number one
Kenneth L. Baker, Kathleen L. Petersen
We determine the PSL_2(C) and SL_2(C) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling…
On well-rounded ideal lattices
Lenny Fukshansky, Kathleen Petersen
We investigate a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded…
Equidistribution of Algebraic Numbers of Norm One in Quadratic Number Fields
Kathleen L. Petersen, Christopher D. Sinclair
Given a fixed quadratic extension K of Q, we consider the distribution of elements in K of norm 1 (denoted N). When K is an imaginary quadratic extension, N is naturally embedded i…
Path count asymptotics and Stirling numbers
K. Petersen, A. Varchenko
We obtain formulas for the growth rate of the numbers of certain paths in infinite graphs built on the two-dimensional Eulerian graph. Corollaries are identities relating Stirling…
On Character varieties of two-bridge knot groups
Melissa L. Macasieb, Kathleen L. Petersen, Ronald M. van Luijk
We find explicit models for the PSL(2,C)- and SL(2,C)-character varieties of the fundamental groups of complements in S^3 of an infinite family of two-bridge knots that contains th…
Conjugate Reciprocal Polynomials with all Roots on the Unit Circle
Kathleen L. Petersen, Christopher D. Sinclair
We study the geometry, topology and Lebesgue measure of the set of monic conjugate reciprocal polynomials of fixed degree with all roots on the unit circle. The set of such polynom…