Vincent Pigno

activity

20142018

most citedEvaluating Binomial Character Sums Modulo Powers of Two

4 citations · 11 across the 5 of their papers we have counts for

collaborators

7 papers

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.DG2017★ 2 cited

Length spectra of sub-Riemannian metrics on compact Lie groups

András Domokos, Matthew Krauel, Vincent Pigno +2

Length spectra for Riemannian metrics are well studied, while sub-Riemannian length spectra have been largely unexplored. Here we give the length spectrum for a canonical sub-Riema…

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

Minimal Mahler measure in real quadratic fields

Todd Cochrane, RMS Dissanayake, Nicholas Donohoue +4

We consider upper and lower bounds on the minimal height of an irrational number lying in a particular real quadratic field.

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 Lind-Lehmer Constant for Z2r​×Z4s​