Year: 2014
Type: article
Abstract: We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for | q 0 | = ... = | q N - 1 | = 1 the quantity Φ = ∑ i + k = j + l q i q k q j q l satisfies Φ ≥ N 2 , with equality if and only if q = ( q i ) is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of Φ , (2) the study of the critical points of Φ , and (3) the computation of the moments of Φ . We explore here these questions, with some results and conjectures.
DOI: 10.5802/ambp.334
Language: French
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2963334995