Cyclic p-roots of prime lengths p and related complex Hadamard matrices
Commutative Algebra
2008-03-19 v1 Number Theory
Operator Algebras
Abstract
In this paper it is proved, that for every prime number p, the set of cyclic p-roots in C^p is finite. Moreover the number of cyclic p-roots counted with multiplicity is equal to (2p-2)!/(p-1)!^2. In particular, the number of complex circulant Hadamard matrices of size p, with diagonal entries equal to 1, is less or equal to (2p-2)!/(p-1)!^2.
Keywords
Cite
@article{arxiv.0803.2629,
title = {Cyclic p-roots of prime lengths p and related complex Hadamard matrices},
author = {Uffe Haagerup},
journal= {arXiv preprint arXiv:0803.2629},
year = {2008}
}