Christopher G. Pinner

activity

20142026

most citedMinimal Group Determinants For Dicyclic Groups

12 citations · 39 across the 18 of their papers we have counts for

collaborators

22 papers

math.NT2026

The integer group determinants for $Z_{p}^{n}$

Michael J. Mossinghoff, Christopher Pinner

We give new conditions on allowable powers of a prime $p$ dividing an integer group determinant for the group $Z_{p}^{n}$ , and show these conditions are sharp for $n \leq 5$ . T…

math.NT2023★ 1 cited

The integer group determinants for the non-abelian groups of order 18

Bishnu Paudel, Chris Pinner

We obtain a complete description of the integer group determinants for the non-abelian groups of order 18.

math.NT2023★ 1 cited

The integer group determinants for the semidihedral group of order 16

Humberto Bautista Serrano, Bishnu Paudel, Chris Pinner

We obtain a complete description of the integer group determinants for SmallGroup(16,8), the semidihedral group of order 16. While this paper was in preparation, a complete descrip…

math.NT2023★ 1 cited

The integer group determinants for SmallGroup(16,13)

Humberto Bautista Serrano, Bishnu Paudel, Chris Pinner

We obtain a complete description of the integer group determinants for SmallGroup(16,13), the central product of the dihedral group of order eight and cyclic group of order four. T…

math.NT2023★ 2 cited

The integer group determinants for $Q_{16}$

Bishnu Paudel, Christopher Pinner

We obtain a complete description of the integer group determinants for $Q_{16},$ the dicyclic or generalized quaternion group of order 16.

math.NT2023

An upper bound on the inhomogeneous approximation constants

Bishnu Paudel, Chris Pinner

For an irrational real $α$ and $γ \neq \in Z + Z α$ it is well known that $∣ n ∣ \to \infty lim inf ∣ n ∣∣∣ n α - γ ∣∣ \leq \frac{1}{4} .$ If the partial quotient…

math.NT2023

Bounding the Largest Inhomogeneous Approximation Constant

Bishnu Paudel, Chris Pinner

For a given irrational number $α$ and a real number $γ$ in $(0, 1)$ one defines the two-sided inhomogeneous approximation constant \begin{equation*} M(α,γ):=\liminf_{|n|\rightarrow\…

math.NT2022

The group determinants for $Z_{n} \times H$

Bishnu Paudel, Christopher Pinner

Let $Z_{n}$ denote the cyclic group of order $n$ . We show how the group determinant for $G = Z_{n} \times H$ can be simply written in terms of the group determinant for…

math.NT2022★ 3 cited

Prime power order circulant determinants

Michael J. Mossinghoff, Christopher Pinner

Newman showed that for primes $p \geq 5$ an integral circulant determinant of prime power order $p^{t}$ cannot take the value $p^{t + 1}$ once $t \geq 2.$ We show that many other values…

math.NT2021

The Integer group determinants for the Heisenberg group of order $p^{3}$

Michael J. Mossinghoff, Christopher Pinner

We establish a congruence satisfied by the integer group determinants for the non-abelian Heisenberg group of order $p^{3}$ . We characterize all determinant values coprime to $p$ , gi…

math.NT2021★ 5 cited

Integer circulant determinants of order 15

Bishnu Paudel, Chris Pinner

We consider the values taken by $n \times n$ circulant determinants with integer entries when $n$ is the product of two distinct odd primes $p, q$ . These correspond to the integer gr…

math.NT2021★ 12 cited

Minimal Group Determinants For Dicyclic Groups

Bishnu Paudel, Chris Pinner

We determine the minimal non-trivial integer group determinant for the dicyclic group of order $4 n$ when $n$ is odd. We also discuss the set of all integer group determinants for t…

math.NT2018

The integer group determinants for the symmetric group of degree four

Christopher Pinner

For the symmetric group $S_{4}$ we determine all the integer values taken by its group determinant when the matrix entries are integers.

math.NT2018

Integer group determinants for small groups

Christopher Pinner, Christopher Smyth

For every group of order at most 14 we determine the values taken by its group determinant when its variables are integers.

math.NT2018★ 1 cited

The Lind-Lehmer Constant for $Z_{2}^{r} \times Z_{4}^{s}$

Michael J. Mossinghoff, Vincent Pigno, Christopher Pinner

We show that the minimal positive logarithmic Lind-Mahler measure for a group of the form $G = Z_{2}^{r} \times Z_{4}^{s}$ with $∣ G ∣ \geq 4$ is $\frac{1}{∣ G ∣} lo g (∣ G ∣ - 1) .$ We…

math.NT2018

A generalization of the Goresky-Klapper conjecture, Part I

Badria Alsulmi, Todd Cochrane, Michael J. Mossinghoff +4

For a fixed integer $n \geq 2,$ we show that a permutation of the least residues mod $p$ of the form $f (x) = A x^{k}$ mod $p$ cannot map a residue class mod $n$ to just one residue class…

math.NT2018★ 4 cited

Minimal group determinants and the Lind-Lehmer problem for dihedral groups

Ton Boerkoel, Christopher Pinner

We find the minimal non-trivial integer variable group determinant for any dihedral group of order less than $3.79 \times 1 0^{47}$ . We think of this as the Lind-Lehmer problem for t…

math.NT2016

On the inhomogeneous spectrum of period two quadratics

Chris Pinner

We give a complete description of the inhomogeneous spectrum of period two quadratics down to the first limit point.

math.NT2016★ 1 cited

Lower bounds on the two-sided inhomogeneous approximation constant

Chris Pinner

We give lower bounds on the case of worst inhomogeneous approximation.

math.NT2014

Binomial Character Sums Modulo Prime Powers

Vincent Pigno, Christopher Pinner

We show that the binomial and related multiplicative character sums $(x, p) = 1 x = 1 \sum p^{m} χ (x^{l} (A x^{k} + B)^{w}), x = 1 \sum p^{m} χ_{1} (x) χ_{2} (A x^{k} + B),$ …

math.NT2014★ 4 cited

Evaluating Prime Power Gauss and Jacobi Sums

Misty Long, Vincent Pigno, Christopher Pinner

We show that for any mod $p^{m}$ characters, $χ_{1}, \dots, χ_{k},$ the Jacobi sum, $x_{1} = 1 \sum p^{m} \dots x_{k} = 1 x_{1} + \dots + x_{k} = B \sum p^{m} χ_{1} (x_{1}) \dots χ_{k} (x_{k}),$ ha…

math.NT2014★ 4 cited

Evaluating Binomial Character Sums Modulo Powers of Two

Vincent Pigno, Chris Pinner, Joe Sheppard

We show that for any mod $2^{m}$ characters, $χ_{1}, χ_{2},$ the complete exponential sum, $x = 1 \sum 2^{m} χ_{1} (x) χ_{2} (A x^{k} + B),$ has a simple explicit evaluation.

The integer group determinants for Zpn​

The integer group determinants for the non-abelian groups of order 18

The integer group determinants for the semidihedral group of order 16

The integer group determinants for SmallGroup(16,13)

The integer group determinants for Q16​

An upper bound on the inhomogeneous approximation constants

Bounding the Largest Inhomogeneous Approximation Constant

The group determinants for Zn​×H

Prime power order circulant determinants

The Integer group determinants for the Heisenberg group of order p3

Integer circulant determinants of order 15

Minimal Group Determinants For Dicyclic Groups

The integer group determinants for the symmetric group of degree four

Integer group determinants for small groups

The Lind-Lehmer Constant for Z2r​×Z4s​

A generalization of the Goresky-Klapper conjecture, Part I

Minimal group determinants and the Lind-Lehmer problem for dihedral groups

On the inhomogeneous spectrum of period two quadratics

Lower bounds on the two-sided inhomogeneous approximation constant

Binomial Character Sums Modulo Prime Powers

Evaluating Prime Power Gauss and Jacobi Sums

Evaluating Binomial Character Sums Modulo Powers of Two

The integer group determinants for $Z_{p}^{n}$

The integer group determinants for $Q_{16}$

The group determinants for $Z_{n} \times H$

The Integer group determinants for the Heisenberg group of order $p^{3}$

The Lind-Lehmer Constant for $Z_{2}^{r} \times Z_{4}^{s}$