9 citations · 9 across the 4 of their papers we have counts for
4 papers · 1 filter
Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Gary Greaves, Graeme Taylor
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahl…
Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
Graeme Taylor
We give examples of points with particularly low height on elliptic curves over quadratic fields, recovered by a search over elliptic divisibility sequences. The smallest example i…
Lehmer's conjecture for matrices over the ring of integers of some imaginary quadratic fields
G. Taylor
Let $R=\mathcal{O}_{\Q(\sqrt{d})}$ for , squarefree, . We prove Lehmer's conjecture for associated reciprocal polynomials of -matrices; that is, any noncycloto…
Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
Graeme Taylor
We determine all Hermitian $\mathcal{O}_{\Q(\sqrt{d})}$-matrices for which every eigenvalue is in the interval [-2,2], for each d in {-2,-7,-11,-15\}. To do so, we generalise charg…