Cyclic p-roots of prime lengths p and related complex Hadamard matrices

Details Cyclic p-roots of prime lengths p and related complex Hadamard matrices Cyclic p-roots of prime lengths p and related complex Hadamard matrices

2008-03-18

arxiv.org/abs/0803.2629v1

Mathematics

Commutative Algebra

Scientific paper

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.

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