English

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}
}