Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields

…is the less-than-catchy title of my first paper, to appear in the Journal of Algebra. With suitable credentials it can be accessed online through ScienceDirect, otherwise there’s a preprint on the arXiv which is a close approximation. The exact details of the print edition are still being finalised; I should have a limited supply of offprints for the truly keen.

The paper covers the classification of the cyclotomic matrices/graphs for four of the six rings I considered in my thesis, but there have been some improvements to the methods. In particular, the proof that any maximal cyclotomic graph over those rings has all vertices of weighted degree four has been substantially streamlined; and there’s an explicit proof that any cyclotomic graph is contained in a maximal one. A follow-up paper proving Lehmer’s conjecture for polynomials arising from such graphs over the same rings is in preparation.

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