Just a brief note that my second paper on my thesis topic has been accepted by the Journal of Number Theory. The full citation is: Graeme Taylor, Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields, Journal of Number Theory, Volume 132, Issue 4, April 2012, Pages 590-607, ISSN 0022-314X, [...]
Archive of posts filed under the Number Theory category.
New records for integral multiples of points
I’ve been trying to extend the results of the work described in the previous post, and following a suggestion of Noam Elkies have changed my search strategy from points corresponding to simple EDS triples to those given by (A,u,c) parametrisations as described here. Experimenting with these revealed some serious deficiencies with the height function in [...]
Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
I have uploaded a preprint of my third paper to the arXiv. In a break from my cyclotomic matrix work, this revisits a project I first became interested in over four years ago: the search for points with small height on elliptic curves over number fields, through the use of elliptic divisibility sequences. There used [...]
The Smoothness Spiral
I’d recently ordered Ben Fry‘s Visualizing Data and started reading it this weekend; just a few pages in I learnt how to import data to processing and a project was born… Since New Orleans I’ve been increasingly interested in mathematical art, and whether in particular I could create something interactive. Here’s what I’ve come up [...]
Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
Online access to my first paper.
Cyclotomic Matrices and Graphs: Warwick
I’m continuing to tour my Cyclotomic Matrices and Graphs talk; today I presented it at the University of Warwick. Here’s the latest and greatest iteration of the slides, mostly unchanged except for the current state of the computer search for minimal noncyclotomics of at most ten vertices. I’d hoped to finish that this month, but [...]
Joint Mathematics Meetings 2011
I spent last week in New Orleans for the Joint Mathematics Meetings 2011. I’d made a rather last minute booking after noticing a couple of sessions could be useful, and hadn’t quite grasped the scale of the event. I’d normally think of 200 mathematicians as a large gathering, but the JMM had over six thousand [...]
Talks on Cyclotomic Matrices and Graphs
I’m speaking this afternoon at the Heilbronn Seminar in Bristol: my slides are available here. This is essentially (up to permutation, and modulo errors!) the talk I gave at Royal Holloway in October, although the last few slides have been replaced with a result I’ve found since then. I try to avoid technical details of [...]
The Diverse Faces of Arithmetic- Notes on Sequences
View as: At The Diverse Faces of Arithmetic there were a pair of (early morning!) overview lectures for postgraduates. I’ve finally got around to typesetting my notes from the first, Tom Ward’s session on recurrence sequences, available as pdf via the above link. The topics included are divisibilty sequences and primitive divisors; linear recurrences; elliptic [...]
MAGIC Talk
Slides for a talk on cyclotomic matrices/graphs given at the MAGIC conference in Manchester.
